Solve the problem. 12) Write an expression for the area of the shaded region and express it in factored form.
9
9
9
9
9
9
12)
9
9
5y
5y
B) (5y - 9)2 D) (5y + 18)(5y - 18)
A) (5y + 9)(5y - 9) C) (5y - 18)2
13) The formula v = 2.5r models the safe maximum speed, v, in miles per hour, at which a car can
13)
travel on a curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an exit ramp as 360 feet. What is the maximum safe speed? A) 30 miles per hour B) 27 miles per hour
C) 35 miles per hour
D) 36 miles per hour
Add or subtract as indicated. 2 7 14) + x2 - 3x + 2 x2 - 1
14)
A)
28x - 12 (x - 1)(x + 1)(x - 2)
B)
9x - 12 (x - 1)(x - 2)
C)
12x - 9 (x - 1)(x + 1)(x - 2)
D)
9x - 12 (x - 1)(x + 1)(x - 2)
List all numbers from the given set B that are members of the given Real Number subset. 15) B = {14, 5, -11, 0, 1 , 25, 0.8, 0.44} Irrational numbers 2
A) 5, 25, 0.44
C) 5, 25, 0.8
B) 5
15)
D) 5, 0.8
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 16) 88 and -92 16) A) |-88 + (-92)| = 4 B) |88 + (-92)| = -4
C) |(-92) - 88| = -180
D) |88 - (-92)| = 180
Find the product.
17) (2 + 11x)2 A) 4x2 + 44x + 121 C) 4 + 44x + 121x2
17) B) 4 + 44x + 11x2 D) 4 + 121x2
3
Simplify the exponential expression. 3 -3 18) 3x y2 6
A) 27y x9
18) B) 27x
9
y6
2 C) y
6 D) y
C) 19
D) 0
27x9
Rewrite the expression without absolute value bars. 19) |-19| A) -19 B) 38
27x9
19)
Simplify by reducing the index of the radical. 8 20) 25x2 4 A) 1 B) 5x 625x
20) 4
C) 5 5x
Evaluate the algebraic expression for the given value or values of the variable(s). 21) 7x - 6; x = -2 A) 8 B) -8 C) 20
D) 5x
21) D) -20
Add or subtract as indicated. 5x 10 22) 2 2 x - 5x + 6 x - 5x + 6
A)
5(x - 2) (x + 2)(x - 3)
22) B)
5(x + 2) (x - 2)(x - 3)
C)
Write the number in scientific notation. 23) 8,546,930 A) 8.54693 × 101 B) 8.54693 × 10-6
5 x-3
D)
5 x-2
23) C) 8.54693 × 106
D) 8.54693 × 107
Evaluate the radical expressions or indicate that the root is not a real number. 3 24) (2)3 A) 2 B) 8
D) not a real number
C) -2 Simplify the exponential expression. 25) (23 )-4
A) -24
24)
25) C) 1 4096
B) -32
4
D) 1 128
Factor completely, or state that the polynomial is prime. 26) 147x2 - 108
26) B) 3(7x - 6)2 D) 3(7x + 6)2
A) prime C) 3(7x + 6)(7x - 6) Add or subtract as indicated. 27) 2 - 6 x+3 x-3
A)
-4x + 24 (x + 3)(x - 3)
27) B)
-4 (x + 3)(x - 3)
C)
Determine whether the statement is true or false. 28) 24 < -24 A) True
-4x + 12 (x + 3)(x - 3)
D)
-4x - 24 (x + 3)(x - 3)
28) B) False
Multiply or divide as indicated. 29) 6x - 2 · x - 2 2x - 4 18x - 6
A) 1 3
29) B) 1
C) x - 2
6
6(x + 2)
D) 6
State the name of the property illustrated. 30) 25 + (8 + 13) = (25 + 8) + 13 A) Commutative property of addition
30)
B) Identity property of addition C) Distributive property of multiplication over addition D) Associative property of addition Perform the indicated operations. 31) (7x4 + 5xy - y3 ) - (x4 + 9xy + 5y3)
31)
A) 6x4 - 4xy - 6y3
B) 8x4 + 13xy + 4y3
C) 6x4 - 4xy - 4y3
D) 7x4 - 4xy - 6y3
Factor the difference of two squares. 32) x2 - 100
A) (x + 10)2
32) C) (x - 10)2
B) (x + 10)(x - 10)
Factor out the greatest common factor. 33) x(x + 8) + 9(x +8) A) (x2 + 8x) + (9x + 72)
D) prime
33) B) 8x(x + 9) D) 9x(x +8)
C) (x +8)(x + 9)
5
Perform the indicated operations. Write the resulting polynomial in standard form. 34) (2x2 + 4x + 7) + (2x2 + 8x + 8) - (5x + 2)
A) 2x2 + 7x + 17
B) 4x2 + 7x + 13
C) 2x2 + 7x + 13
34) D) 4x2 + 7x + 17
Add or subtract as indicated. 2 35) x - 9x + 18 x-6 x-6
35) 2
B) x - 9x + 18
A) x + 3
C) x - 6
x-6
D) x - 3
Use the product rule to simplify the expression. 36) 486x2
A) 9 x 6
36) C) 9x2 6
B) 9 6
D) 9 6x2
Solve the problem. 37) Write an expression for the area of the shaded region and express it in factored form. 9y x
37)
9y
x
9y
x 9y
A) x2 + 18xy + 81y2 C) (x + 9y)2
B) x2 + 9xy + 81y2 D) 9(x + y)2
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 38) 6x-1 - 4 + 6x
A) Yes; 6x + 6x-1 - 4
38)
B) No
Factor the trinomial, or state that the trinomial is prime. 39) 12x2 + 17xy + 6y2
39)
A) (12x + 2y)(x + 3y) C) (3x - 2y)(4x - 3y)
B) (3x + 2y)(4x + 3y) D) prime
Find the product.
40) (9x - 5y)2 A) 81x2 - 90xy + 25y2 C) 81x2 + 25y2
40) B) 9x2 + 25y2 D) 9x2 - 90xy + 25y2 6
Find all numbers that must be excluded from the domain of the rational expression. 41) x - 4 x2 - 16
B) x 1
A) x 4, x -4
C) x 16
4
41) D) x 4
Write the number in decimal notation without the use of exponents. 42) 9 × 10-3
A) 900
B) 0.009
C) 9000
42) D) 0.09
Rationalize the denominator. 5
43)
A) 5 5 Solve.
43)
5
B) 5
C) 1
D) 5
44) The formula C = 5 (F - 32) expresses the relationship between Fahrenheit temperature, F, and 9
44)
Celsius temperature, C. Use the formula to convert 59°F to its equivalent temperature on the Celsius scale. A) 51°C B) 15°C C) 3°C D) 49°C
Evaluate the expression or indicate that the root is not a real number. 45) (4)2
A) 256
B) 4
C) 1
D) Not a real number
16
45)
Simplify the exponential expression. x2
46)
46)
x5
A) - 1
x3
47) -7 0 A) 0 48) -56x
B) x3
C) -x3
D) 1
x3
47) B) 7
C) -1
D) 1
3
48)
8x8
A) -7x5
B) -7
C) -7x4
x4
7
D) -7 x5
Write the number in scientific notation. 49) 0.00002686 A) 2.686 × 104 B) 2.686 × 105
49) C) 2.686 × 10-4
D) 2.686 × 10-5
Use the quotient rule to simplify the expression. 54x3
50)
50)
6x
A) 6x2
C) 3x
B) 3 x 6
2
6
D) 3 x
Factor using the formula for the sum or difference of two cubes. 51) 125x3 + 27
A) (5x - 3)(25x2 + 15x + 9) C) (5x + 3)(25x2 + 9)
51)
B) (5x + 3)(25x2 + 15x + 9) D) (5x + 3)(25x2 - 15x + 9)
Find all numbers that must be excluded from the domain of the rational expression. 52) 5 x+8
A) x -8
B) x 8
C) x -5
Factor out the greatest common factor. 53) x2 (x - 13) - (x - 13)
52) D) x 0
53)
A) (x - 13)(x2 - 1)
B) x2 (x - 13)
C) (x - 13)(x2 + 1)
D) (x3 - 13x2 ) - (x - 13)
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 2x + 2 54) 54) 2 10x + 18x + 8
A) 2x + 5 , x - 18 5x + 18
C)
5
1 4 ,x - ,x - 1 5x + 4 5
B)
2x + 2 4 ,x - ,x - 1 5 10x2 + 18x + 8
D)
2x 4 ,x 5x + 4 5
Factor completely, or state that the polynomial is prime. 55) 64x2 - 176x + 121 - 81y2
55)
A) (8x - 11 + 9y)(8x - 11 - 9y) C) (8x + 11 + 9y)(8x + 11 - 9y)
B) (8x + 11 + 9y)(8x - 11 - 9y) D) prime
Factor by grouping. Assume any variable exponents represent whole numbers. 56) x3 + 8x - 5x2 - 40
A) (x - 5)(x2 + 8)
B) (x + 5)(x2 + 8)
C) (x - 5)(x + 8)
8
56) D) (x - 5)(x2 - 8)
Solve the problem. 57) Write a polynomial in standard form that represents the volume of the open box.
57)
x
12 - 2x
4 - 2x
A) 2x3 - 32x2 + 48x C) 4x3 + 32x2 + 48x
B) 4x2 - 32x + 48 D) 4x3 - 32x2 + 48x
Evaluate the radical expressions or indicate that the root is not a real number. 4 58) 256 A) 256 B) 4
58)
D) not a real number
C) -4
Perform the indicated operations. Write the resulting polynomial in standard form. 59) (-3x8 - 5x7 + 4x6 - 3) + (6x8 - 9x7 + 2x6 - 6)
A) 9x8 - 4x7 - 2x6 - 3 C) 3x8 - 14x7 + 6x6 - 9
Find the product. 60) (x + 9)(x - 9) A) x2 - 81
B) 3x8 - 4x7 - 2x6 - 3 D) 9x8 - 4x7 - 2x6 - 9
60) B) x2 - 18
C) x2 + 18x - 81
Write the algebraic expression without parentheses. 61) -(4x - 2) A) -4x - 2 B) -4x + 2 Find the intersection of the two sets. 62) {9, 11, 12, 14} A) {9, 11}
Simplify the exponential expression. 64) 33 · 3 9
A) 327
D) x2 - 18x - 81
61) C) 4x - 2
D) 8x
62) C) {9, 11, 12, 14}
B)
Factor completely, or state that the polynomial is prime. 63) x2 + 4
A) (x + 2)(x - 2)
59)
D) {12, 14}
63)
B) (x - 2)2
C) (x + 2)2
D) prime
64) B) 312
C) 927
9
D) 912
Factor and simplify the algebraic expression. 65) (x + 7)2/5 - (x + 7)12/5
65)
A) (x + 7)2/5 (- x2 - 14x - 48) C) (x + 7)12/5 ((x + 7)1/6 - 1)
B) (x + 7)(- x2 - 14x + 48) D) (x + 7)((x + 7)2/5 - (x + 7)12/5)
Factor the trinomial, or state that the trinomial is prime. 66) 3x2 - 14x + 16
A) (3x - 8)(3x + 2)
66)
B) (3x + 2)(x - 8)
C) (3x - 8)(x - 2)
Find the product. 67) (5x2 - 1)(7x2 + 4)
D) 3(x - 8)(x - 2)
67)
A) 35x4 + 13x2 + 13
B) 35x4 + 13x2 - 4
C) 35x2 + 13x - 4
D) 12x4 + 13x2 - 4
Multiply or divide as indicated. 2 68) 5x - 5 · 4x x 8x - 8
68) 3
2
A) 40x + 80x + 40
B) 20x - 20x
C) 5x
D) 2
2
8x2 - 8x
4x3
2
5x
Use the product rule to simplify the expression. 69) 2x2 · 6x
A) 2 x 3x
69)
B) 2 x 3x2
C) 2x2 3x
Simplify the exponential expression. 70) x9 · x2
A) x11
D) 2 x 3
70) B) 11x
C) 18x
D) x18
Multiply or divide as indicated. 2 2 71) x + 15x + 54 · x + 5x + 6 x2 + 8x + 12 x2 + 12x + 27
A)
1 x+3
71) C) x + 2
B) 1
x+3
Find the product. 72) (5x2 + 12)2
D) x + 9 x+2
72)
A) 25x2 + 120x + 144
B) 5x4 + 120x2 + 144
C) 25x4 + 144
D) 25x4 + 120x2 + 144
10
Factor completely, or state that the polynomial is prime. 73) 2x3 - 18a 2 x + 8x2 + 8x
73)
A) 2x(x + 2 + 3a)(x - 2 - 3a) C) 2x(x + 2 + 3a)(x + 2 - 3a)
B) 2x(x + 2 + 3a)(x - 2 + 3a) D) prime
Factor out the greatest common factor. 74) 21x4 - 6x3 + 15x2
74)
A) 3x2 (7x2 - 2x + 5)
B) x2 (21x2 - 6x + 15)
C) 3x(7x3 - 2x2 + 5x)
D) 3(7x4 - 2x3 + 5x2 )
Add or subtract terms whenever possible. 75) 8 3 - 6 12 A) 4 3 B) -4 3
75) C) 2 3
D) -20 3
C) (x - 2)(x - 3)
D) prime
Factor the trinomial, or state that the trinomial is prime. 76) x2 - 5x + 6
A) (x + 2)(x + 1)
76)
B) (x + 2)(x - 3)
Find the degree of the polynomial. 77) -4x + 8x6 - 5x5 - 21
A) degree 4
77) B) degree 6
C) degree 8
D) degree 5
Evaluate the radical expressions or indicate that the root is not a real number. 3 78) -125 A) 5 B) -125
D) not a real number
C) -5 Factor and simplify the algebraic expression. 79) (x + 6)-1/3 - (x + 6)-2/3
79) 1/3 B) (x+ 6) - 1 (x+ 6)1/3
A) (x + 6)-1/3 - (x + 6)-2/3 C)
78)
1/3 - 1
D) (x+ 6)
x+5 (x+ 6)2/3
(x+ 6)2/3
Solve the problem. 80) A department store is having a clearance sale. The price on a television is reduced by 32%. That sale price is then reduced by another 32%. If x is the television's original price, the sale price can be represented by (x - 0.32x) - 0.32(x - 0.32x). With these two reductions, at what percentage of the original price is the television being sold? Use the factored, simplified form of the expression to answer the question. A) 68% B) 36% C) 64% D) 46.24%
11
80)
Simplify the exponential expression. 81) x2 y-4
A)
x2
y10
81) B) y10x2
C)
Factor completely, or state that the polynomial is prime. 82) 48y4 - 27y2
x2 y4
D) y4 x2
82)
A) 3y2 (4y - 3)2 C) 3y2 (4y + 3)(4y - 3)
B) 3(4y2 + 3)(4y2 - 3) D) prime
Add or subtract as indicated. 4x + 2 3x - 6 83) 2 2 x + 13x + 40 x + 13x + 40
A)
x-8 2 x + 13x + 40
B)
83) 1 x+8
C)
1 2 x + 13x + 40
D)
1 x+5
Simplify the exponential expression. -36x 8
84)
84)
4x3
A) x4
B) x5
C) -9x5
Find the product. 85) (2x2 - 5)2
85)
A) 4x2 - 20x + 25
B) 4x4 - 20x2 - 25
C) 4x4 + 20x2 + 25
D) 4x4 - 20x2 + 25
Simplify the exponential expression. 86) (x5 )6 A) x11
D) -9x4
86) B) 6x5
C) 6x30
D) x30
Perform the indicated computation. Write the answer in scientific notation. 8.37 × 10-3
87)
87)
3.1 × 10-8
A) 5.4 × 10-11
C) 2.7 × 105
B) 2.7 × 10-11
D) 5.4 × 105
Add or subtract as indicated. 2 88) x - 12 + 2x - 3 x2 - 3x - 40 x2 - 3x - 40
A) x - 3 x-8
88) B)
C) ( x - 5)( x + 3)
x-3
x2 - 3x - 40
( x + 5)( x - 8)
12
D) x + 5
x-8
Factor and simplify the algebraic expression. 89) x6/7 - x1/7
A) x1/7 (x5/7 - 1)
89)
B) x6/7 (1 - x 5/7 )
C) x(x 5/7 - 1)
Factor the perfect square trinomial. 90) 100x2 + 20x + 1
D) x1/7 (x6 - 1)
90) B) (10x + 1)2 D) prime
A) (10x + 1)(10x - 1) C) (x + 10)2 Simplify the exponential expression. x-3
91)
91)
y-2
A) x
3
2
B) y
y2
C)
x3
1 3 x y2
D) x3 y2
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 92) 33 · 8
A) 35
B) 13,824
C) 72
92)
D) 216
Simplify the exponential expression. 6 12 0 93) 36x y 4x3 y9
A) x3 y3
93) C) 9x3 y3
B) 1
D) 0
Add or subtract as indicated. 94) 3x - 24 x-8 x-8
A) 3x
94) C) 3x - 24
B) 3
x - 16
D) 1 3
Multiply or divide as indicated. 2 2 95) (x + 3) ÷ x - 9 x-3 3x - 9 2
A) 6(x + 9) x2 - 9
95) 2
C) (x + 3)
B) 3(x + 3) x-3
(x - 3)2
3
D) (x + 3)
3(x - 3)
Factor and simplify the algebraic expression. 96) 7x-2/3 + 63 x1/3
A) 1 + 7x 9x2/3
96)
B) 9 + x
C) 7(9x + 1)
7x1/3
x2/3
13
D) 1 + 9x
1/3
7x2/3
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 2 -8 x-4 y2
97)
97)
2 -5 x-7 y4
A)
8 x3 y2
B) x
3
C) 3x
8y2
3
D)
y2
1 8x7 y2
Simplify the exponential expression. -18x 7 y8
98)
98)
6x2 y5
A) -3x4 y2
B) x5 y3
C) -3x5 y3
D) -3x4 y5
Add or subtract as indicated. 8x - 3 -5 - 7x 99) + x2 - 13x + 40 x2 - 13x + 40
A)
1 x-5
B)
99) 1 x-8
C)
1
x2 - 13x + 40
D)
x+8
x2 - 13x + 40
Simplify the exponential expression. 54x12y10z 5
100)
100)
9x7 y4 z 4
A) 6x5 y6
B) 6x5 y6z
C) x5 y6 z
D) 6x4 y5z
Perform the indicated operations. Write the resulting polynomial in standard form. 101) (8x7 + 9x6 - 8) - (2x7 - 6x6 - 16)
A) 6x7 + 15x6 - 24
B) 6x7 + 15x6 + 8
C) 29x13
D) 6x7 + 11x6 - 24
101)
State the name of the property illustrated. 102) (7 · 17) · 2 = 7 · (17 · 2) A) Identity property of multiplication
102)
B) Associative property of multiplication C) Commutative property of multiplication D) Distributive property of multiplication over addition Simplify the exponential expression. 103) y · y12
A) 2y13
103) B) 2y12
C) y12
D) y13
Write the number in decimal notation without the use of exponents. 104) -7.1039 × 105
A) -355.195
B) -71,039
C) -710,390
14
104) D) -7,103,900
Evaluate the expression without using a calculator. 105) 36-3/2
A) - 1
216
105) C) 1
B) -216
216
D) 216
Factor and simplify the algebraic expression. 106) (x + 9)-1/5 + (x + 9)-6/5
106)
A) (x + 9)6/5(x + 10)
B) (x + 9)-1/5 + (x + 9)-6/5
C) (x + 10)
D) (x + 10)
(x+ 9)1/5
(x+ 9)6/5
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 5 -2 107) xy x3 y
A)
1 8 x y12
B) x
4
8
y8
107)
C) y
D)
C) 25x2 - 10x + 25
D) x2 + 25
x4
1 5 x y11
Find the product.
108) (x - 5)2 A) x2 - 10x + 25
Find the union of the two sets. 109) {1, 11} {1, 5, 9} A) {1}
108) B) x + 25
109) C) {1, 5, 9, 11}
B)
D) {5, 9, 11}
State the name of the property illustrated. 110) 1 (x + 3) = 1, x -3 (x + 3)
110)
A) Identity property of multiplication C) Inverse property of addition
B) Commutative property of multiplication D) Inverse property of multiplication
Evaluate the expression or indicate that the root is not a real number. 111) - 400 A) 20 B) -20
111)
D) Not a real number
C) -200 Rationalize the denominator. 112) 1 3
A) 1 + 3
112) B) 1 + 3
C) 3
3
15
D)
3 3
Simplify the complex rational expression. x xx+3
113)
113)
x+2
A)
x x+2
B)
2 C) x
x x-3
x+3
D)
x x+3
Simplify the exponential expression. 114) (-9)0
A) 1
114) C) 9
B) -1
D) 0
Solve the problem. 115) Write an expression for the area of the shaded region and express it in factored form.
7
115)
y
7 y
A) y2 + 49
C) (y - 7)2
B) (y + 7)(y - 7)
D) (y + 7)2
Evaluate the algebraic expression for the given value or values of the variable(s). 116) x2 - 4(x - y); x = 8 and y = 3
A) 44
C) 29
B) -84
116) D) 35
Rationalize the denominator. 7 117) 6 + 13
A) 13 + 6
117) B) 6 - 13
C) 13 - 6
D) 7
Simplify the complex rational expression. 49y2 - 36x2
118)
xy
118)
7 6 x y
A) 6x + 7y
B) 6x + 7y
C) 7x + 6y
xy
D)
xy 7x + 6y
Factor the trinomial, or state that the trinomial is prime. 119) x2 - 6x + 8
A) (x - 2)(x - 4)
119)
B) (x + 2)(x + 1)
C) (x + 2)(x - 4)
16
D) prime
Simplify the exponential expression. 120) 5x-2 y9
A)
5 2 x y9
120) 9 B) y 5x2
Add or subtract terms whenever possible. 121) 8 2 - 4 2 A) 12 2 B) 4 2
D)
C) -32 4
D) 4 4
C) - 1 16
D) 1 16
y9
122) B) -16
Perform the indicated computation. Write the answer in scientific notation. 123) (2 × 105 )(3.6 × 108 )
A) 7.2 × 1040
5x2
121)
Simplify the exponential expression. 122) (-2)-4
A) 16
9 C) 5y x2
B) 7.2 × 1013
C) 7.2 × 1014
123) D) 72 × 1013
Evaluate the radical expressions or indicate that the root is not a real number. 4 124) (-5)4 A) -5 B) 5
C) 625
124)
D) not a real number
Evaluate the expression without using a calculator. 125) 644/3
A) 16,384
125)
B) 1024
C) 256
D) 4096
Multiply or divide as indicated. 3 126) x + 1 · 9x x3 - x2 + x -45x - 45 3
A) - x + 1
5(x + 1)
126) 2
B) - 1
C) - x + 1
D)
B) b
C) 14
D) 1
C) 8 3
D) -2x 6
5
5
x+1 5(-x - 1)
Simplify the exponential expression. 127) (14b)0
A) 0
127)
Add or subtract terms whenever possible. 128) 3 3x - 5 3x A) -2 3x B) -15 6x
128)
17
Simplify the exponential expression. 2 129) - 3 x
A) 9
x
129) B) 3
C) - 9
x2
x2
D) 9
x2
Rationalize the denominator. 130) 7 3
A) 21
130) B) 7
C)
21 3
D)
21 9
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places. 131) Approximately 4 × 103 employees of a certain company average $30,000 each year in salary. What is the total amount earned by all the employees of this company per year? A) $1.2 × 108 B) $1.2 × 109 C) $12 × 109
Determine whether the statement is true or false. 132) 17 > 25 A) True
131)
D) $12 × 108
132) B) False
Find the product.
133) (x - 6)(x2 + 6x + 36) A) x3 + 216 C) x3 + 12x2 + 12x - 216
133) B) x3 - 12x2 - 12x - 216 D) x3 - 216
Rewrite the expression without absolute value bars. 134) |16| A) -16 B) 32
134) C) 0
D) 16
Find the product.
135) (x + y)(x2 - xy + y2 ) A) x3 + 2x2 y + 2xy2 + y3 C) x3 - 2x2 y - 2xy2 + y3
135) B) x3 - y3 D) x3 + y3
Factor the trinomial, or state that the trinomial is prime. 136) 5x2 - 27xy - 18y2
136)
A) (5x + 3y)(x - 6y) C) (5x + 6y)(x - 3y) Simplify the exponential expression. 137) (-4x2 y)(-7x4 y3 )
A) 28x8y3
B) y(5x + 3)(x - 6) D) prime
137) B) 28x6y4
C) -11x6 y3
18
D) -28x6 y3
Evaluate the algebraic expression for the given value or values of the variable(s). 138) 8(x - 5) ; x=7 2x + 2
A) - 3
B) 6
2
C) 2
Simplify the exponential expression. 139) (x-1 y5)-3 2
A) y
D) 1
139) B)
x-4
138)
C) x
1 3 x y15
3
y15
D) x
-4
y2
Find the product.
140) (x - 12)(x2 + 3x - 6) A) x3 - 9x2 - 42x + 72 C) x3 + 15x2 + 30x - 72
140) B) x3 + 15x2 + 42x + 72 D) x3 - 9x2 - 30x - 72
Factor the difference of two squares. 141) 49x2 - 36y2
141)
A) (7x + 6y)2
B) (7x - 6y)2
C) (7x + 6y)(7x - 6y)
D) prime
Simplify the algebraic expression. 142) -5(3r + 4) + 10(9r + 9) A) -2r - 1
142) C) 75r + 70
B) -35r
Rewrite the expression without absolute value bars. 143) 17 - 7 A) 17 - 7 B) 10
D) 75r + 4
143) C) 7 - 17
D) -10
Solve the problem. 144) Racing cyclists use the algebraic expression 4 x to determine the maximum speed, in miles per hour, to turn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist should travel around a corner of radius 18 feet without tipping over. Write the answer in simplified radical form.
A) 12 2 miles per hour
B) 16 + 2 miles per hour
C) 4(4 + 2) miles per hour
D) 16 2 miles per hour
x
19
144)
145) Write an expression for the area of the shaded region and express it in factored form.
A) 5(x - y)2
B) (x - 2y)(x - 3y)
C) (x - y)(x - 3y)
145)
D) (x - 5y)2
Perform the indicated operations. Write the resulting polynomial in standard form. 146) (9x7 + 17x6 - 4) - (6x7 + 10x6 + 16)
A) 3x7 + 7x6 - 20
B) 3x7 + 7x6 + 12
C) 3x7 + 23x6 + 12
D) -10x13
Factor the difference of two squares. 147) 4x2 - 81
A) (2x + 9)(2x - 9)
146)
147) B) (2x + 9)2
C) (2x - 9)2
State the name of the property illustrated. 148) (x + 3) + [-(x + 3)] = 0 A) Inverse property of multiplication
D) prime
148) B) Identity property of multiplication D) Inverse property of addition
C) Commutative property of addition Simplify the exponential expression. -2x 6
149)
149)
y
A) 64x y6
150) x9 · x-5
A) 1 x4
C) -12x
B) -12x y
6
y6
D) 64x
6
y6
150) B) - 1 x4
C) -x4
Find the product. 151) (7xy2 - 3y)(7xy2 + 3y)
D) x4
151)
A) 7x2 y4 - 3y2 C) 49x2y4 - 42xy3 - 9y2
B) 49x2y4 - 9y2 D) 49x2y4 + 42xy3 - 9y2
20
Simplify by reducing the index of the radical. 10 152) x6
A)
5
x3
152)
B) x
C)
5
x
D) x3
Factor out the greatest common factor. 153) 5x2 - 15x
A) 5(x2 - 3x)
153) B) x(5x - 15)
C) 5x(x - 3x)
D) 5x(x - 3)
C) x9
D) 1 x9
Simplify the exponential expression. 154) (x-3 )-3
A) 1 x6
154) B) -x6
Solve the problem. 155) Express the perimeter of the rectangle as a single rational expression.
155)
9 x-3 7 x
A) 32x - 42 x(x - 3)
B) 32x - 42
C) 16x - 21
x(3 - x)
x(x - 3)
D) 16x - 21 x(3 - x)
156) The formula v = 20L can be used to estimate the speed of a car, v, in miles per hour, based on the
156)
length, L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident and its skid marks measure 125 feet, at what estimated speed was the car traveling when it applied its brakes just prior to the accident? A) 45 miles per hour B) 50 miles per hour
C) 60 miles per hour
D) 55 miles per hour
Evaluate the expression or indicate that the root is not a real number. 157) 100 - 36 A) 8 B) 28 C) 14
158) 49
157) D) 64 158)
A) 1
B) 7
C) 2401
D) Not a real number
49
21
Multiply or divide as indicated. 159) 5x · 6x + 3 10x + 5 2
A) 3
159) B) 3x
2
C) x
2
D) 3x
2
Write the algebraic expression without parentheses. 160) -(4v) A) -4v B) 4 - v
10
160) C) 4v
D) -4 - v
Solve the problem. 161) Write a polynomial in standard form that represents the area of the shaded region.
161)
x+9
x+3
A) -7x - 23
x+1
x+4
B) x2 + 22x + 23
C) 7x + 23
D) 17x + 31
Evaluate the algebraic expression for the given value or values of the variable(s). 162) 4x2 + 3y; x = 9 and y = 5
A) 339
B) 127
162)
C) 1680
D) 1311
C) (4x - 3)(3x - 4)
D) prime
Factor the trinomial, or state that the trinomial is prime. 163) 12x2 + 25x + 12
A) (12x + 3)(x + 4)
163)
B) (4x + 3)(3x + 4)
Perform the indicated computation. Write the answer in scientific notation. 164) 80,000,000,000 0.000004
A) 4 × 1015
B) 4 × 1016
C) 2 × 1016
164) D) 2 × 1015
Rationalize the denominator. 165) 16 7
A) 16 7 7
165) C) 4 7
B) 53
7
22
D) 4 7
Factor using the formula for the sum or difference of two cubes. 166) 125x3 - 27
166)
A) (5x + 3)(25x2 - 15x + 9)
B) (5x - 3)(25x2 + 15x + 9)
C) (5x - 3)(25x2 + 9)
D) (5x - 3)(25x2 - 15x + 9)
Simplify the exponential expression. 167) -6y0
A) 0
167) C) 1
B) -5
D) -6
Simplify the complex rational expression. 1 x+2
168)
168)
3 x2 - 4
A)
3 x-2
B) x + 2
C) x - 2
3
D) x - 2 3
Add or subtract as indicated. 169) 11 - 3 x-6 6-x
169)
A) 14
B)
6-x
84 - 14x (x - 6)(6 - x)
C)
8 x-6
D) 14
x-6
Solve the problem. 170) Express the perimeter of the trapezoid as a single rational expression.
170)
x+5 x+3 2 x+3
2 x+3 x+2 x+3
A) 2x + 11 x+3
C) 4x + 11
B) x + 8
x+3
D) x + 11 x+3
Factor the trinomial, or state that the trinomial is prime. 171) 6x2 + 7xy + y2
A) (6x + y)(x + 6y)
171)
B) (6x + y)(x + y)
C) (6x - y)(x - y)
23
D) prime
Find all numbers that must be excluded from the domain of the rational expression. x-7 172) 2 x + 4x - 21
A) x -7, x 3
B) x 7
C) x -3, x 7
172) D) x 0
Solve.
173) A stone is dropped from a tower that is 730 feet high. The formula h = 730 - 16t2 describes the
173)
stone's height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 seconds after it is released? A) 449 ft B) 484 ft C) 499 ft D) 474 ft
Factor completely, or state that the polynomial is prime. 174) 2x3 + 250
174)
A) 2(x3 + 125)
B) 2(x + 5)(x2 - 5x + 25)
C) 2(x + 5)3
D) prime
Write the algebraic expression without parentheses. 175) -(-6 + 4y) A) 6 - 4y B) 6 + 4y
175) C) 24y
D) -6 + 4y
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 176) 3x + 8 x
A) Yes; 8 + 3
176)
B) No
x
Add or subtract as indicated. x+5 2x + 1 177) + 2 2 x + 11x + 28 x + 10x + 21
177) 3x 2 + 17x + 19 (x - 7)(x - 4)(x - 3)
A)
3x + 6 2 2x + 21x + 49
B)
C)
3x 2 + 17x + 19 (x + 7)(x + 4)(x + 3)
D) 3x + 6
Simplify the exponential expression. 178) 5-2
A) -25
178) B) 1
C) 25
10
Simplify using properties of exponents. 179) (6x2/3 )(9x1/2 )
A) 54x7/6
D) 1
25
179)
B) 54x7/5
C) 54x1/2
24
D) 54x2/3
Factor the difference of two squares. 180) x4 - 1
180)
A) (x2 - 1)(x2 - 1)
B) (x2 + 1)(x2 + 1)
C) (x2 + 1)(x + 1)(x - 1)
D) prime
Determine whether the statement is true or false. 181) -7 14 A) True
181) B) False
Factor completely, or state that the polynomial is prime. 182) 4x3 - 484x
182)
A) 4x(x + 11)(x - 11) C) 4(x + 11)(x2 - 11x)
B) x(x + 11)(4x - 44) D) prime
Simplify the exponential expression. -4 -4 183) x y6
A) x
-8
y2
183) 2
B) x16y24
C) y
B) 9
C) 1 9
x-8
184) 3-3 · 3
D)
1 16 x y24
184)
A) 1 27
Perform the indicated operations. 185) (x3 + 3xy - 8y2 ) - (5x3 + 8xy + y2)
D) 27
185)
A) 4x3 + 5xy - 7y2
B) -4x3 - 5xy - 7y2
C) -4x3 - 5xy - 9y2
D) 6x3 - 5xy - 9y2
Use the quotient rule to simplify the expression. 186) 9 16
A)
3 4
B)
186)
3 4
C) 0
D) 3 4
Add or subtract terms whenever possible. 187) 10 8 - 4 200 - 8 98 A) -136 2 B) -76 2
C) 10 2
D) 136 2
Use the product rule to simplify the expression. 188) 325 A) 25 13 B) 65
C) 325
D) 5 13
187)
188)
25
Write the algebraic expression without parentheses. 189) - (7z - 4w + 3y) A) -7z - 4w + 3y B) -7z - 4w - 3y
189) C) -7z + 4w + 3y
Rewrite the expression without absolute value bars. 190) -6 + -7 A) -1 B) 13
D) -7z + 4w - 3y
190) C) 1
D) -13
C) (x - 7)(x - 6)
D) prime
Factor the trinomial, or state that the trinomial is prime. 191) x2 - 13x + 42
A) (x + 7)(x - 6)
191)
B) (x + 7)(x + 1)
Factor completely, or state that the polynomial is prime. 192) y5 - 81y
192)
A) y(y2 - 9)(y2 - 9) C) y(y2 + 9)(y + 3)(y - 3)
B) y(y2 + 9)(y2 + 9) D) prime
Perform the indicated operations. Write the resulting polynomial in standard form. 193) (5x5 + 8x4 - 9x3 + 4) - (3x5 + 4x4 - 2x3 - 9)
A) 8x5 + 12x4 - 11x3 + 13
B) 2x5 + 4x4 - 7x3 + 13
C) 8x5 + 12x4 - 11x3 - 5
D) 2x5 + 12x4 - 11x3 - 5
193)
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. x2 + 6x + 9
194)
194)
x2 + 12x + 27
A) 6x + 1 , x - 1
B) x + 3 , x -9, -3
C) 6x + 9 , x - 9
2 D) - x + 6x + 9 , x -9, -3
12x + 3
12x + 27
4
x+9
4
x2 + 12x + 27
Multiply or divide as indicated. 2 2 195) x + 5x + 6 · x + 5x x2 + 7x + 10 x2 + 11x + 24
A)
1 x+8
195) 2
B) x + 5x
C)
x+8
Factor the difference of two squares. 196) (16x4 - 81)
x
x2 + 7x + 10
D)
x x+8
196)
A) (4x2 + 9)(4x2 - 9)
B) (2x + 3)2 (2x - 3)2 D) (4x2 + 9)(4x2 + 9)
C) (4x2 + 9)(2x + 3)(2x - 3)
26
Perform the indicated operations. Write the resulting polynomial in standard form. 197) (8x6 - 8x5 - 4x4 - 1) + (5x6 - 3x5 + 6x4 + 3)
A) 13x12 - 11x10 + 2x8 + 2
B) -4x6 - 4x5 + 11x4 - 3
C) 13x6 - 11x5 + 2x4 + 2
D) 4x30 + 2
197)
State the name of the property illustrated. 198) -7(5 + 4) = -35 + (-28) A) Associative property of multiplication
198)
B) Associative property of addition C) Distributive property of multiplication over addition D) Commutative property of multiplication Use the product rule to simplify the expression. 199) 14x · 28x A) 14x2 2 B) 14 x 2
199) C) 14 2x2
D) 14 2x
Write the algebraic expression without parentheses. 200) 1 (6x) + [(9x) + (-9x)] 6
A) -17x Find the intersection of the two sets. 201) {1, 10, 9} {5, 11} A) {1, 5, 9, 10, 11}
200)
B) x
C) 19x
D) 1
201) B) {1, 9}
C)
D) {10, 9}
Perform the indicated computation. Write the answer in scientific notation. 14.05 × 107
202)
202)
5 × 10-8
A) 2.81 × 10-1
B) 2.81 × 1015
C) 5.62 × 10-1
D) 5.62 × 1015
Find the product.
203) (3x - 2)3 A) 27x3 + 54x2 + 36x + 8 C) 27x3 - 54x2 + 36x - 8
203) B) 9x2 - 12x + 4 D) 27x3 - 54x2 + 54x - 8
Factor completely, or state that the polynomial is prime. 204) x3 - 4x2 - 9x + 36
204)
A) (x - 4)(x - 3)2 C) (x + 4)(x + 3)(x - 3)
B) (x - 4)(x + 3)(x - 3) D) prime
Find the product.
205) (x + 8)2 A) x2 + 16x + 64
205) C) 64x2 + 16x + 64
B) x + 64 27
D) x2 + 64
State the name of the property illustrated. 206) (4 + 7) + (6 + 14) = (6 + 14) + (4 + 7) A) Inverse property of addition
206)
B) Commutative property of addition C) Associative property of addition D) Distributive property of multiplication over addition Use the quotient rule to simplify the expression. 207) 1 4
A) 4
207) C) 1
B) 2
16
Perform the indicated operations. Write the resulting polynomial in standard form. 208) (-3x5 - 5x2 + 5) + (7x5 + 9x2 + 5)
A) 18x7
Simplify the exponential expression. 209) (x7 y)3 A) x10y
D) 1 2
208)
B) 4x5 + 12x2 + 0
C) 4x5 + 4x2 + 10
D) 4x5 + 4x2 + 0
B) x21y
C) x21y3
D) x10y4
209)
Find the degree of the polynomial. 210) 7x3 - 3x2 - 7x + 3x4 - 5
A) degree 3
210) B) degree 7
C) degree 2
D) degree 4
Solve the problem. 211) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic d expression . Find how long it will take a ball dropped from the top of a building 83 feet tall to 16
211)
hit the ground. Write the answer in simplified radical form. A) 9 + 2 seconds B) 9 2 seconds 4 4
C)
83 seconds 16
D)
83 seconds 4
Multiply or divide as indicated. 2 2 212) x + 11x + 30 ÷ x + 5x x2 + 15x + 54 x2 + 3x - 54
A)
x 2 x + 15x + 54
212) C) x - 6
B) x - 6
x2 + 9x
28
D) x - 6 x
Solve the problem. 213) Find the formula for the volume of the region outside the smaller rectangular solid and inside the larger rectangular solid. Express the volume in factored form.
a
b
213)
b 4a a
A) (4a + b)(4a - b)
C) 4a(a 2 + b2)
B) 4a(a + b)(a - b)
D) 4a(a 2 - b2)
Simplify the exponential expression. x3 4
214)
214)
2
A) x
12
16
B) x
7
C) x
16
12
2
D) x
7
2
Write the number in decimal notation without the use of exponents. 215) -7.84 × 107
A) -784,000,000
B) -78,400,000
C) -7,840,000
215) D) 78,400,000
Evaluate the algebraic expression for the given value or values of the variable(s). 216) (x + 4y)2 ; x = 3 and y = 4
A) 38
B) 49
Write the number in scientific notation. 217) 0.000000041701 A) 4.1701 × 10-8 B) 4.1701 × 10-9
D) 361
C) 4.1701 × 108
D) 4.1701 × 10-7
217)
Factor the perfect square trinomial. 218) x2 - 4x + 16
A) (x + 4)2
216)
C) 19
218) C) (x - 4)2
B) (x + 4)(x - 4)
D) prime
Perform the indicated computation. Write the answer in scientific notation. 10 × 10-8
219)
219)
2 × 10-3
A) 5 × 10-5
B) 10 × 10-5
C) 10 × 10-11
29
D) 5 × 10-11
Find the product.
220) (2x - 7)2 A) 4x2 - 28x + 49
220) B) 2x2 + 49
C) 2x2 - 28x + 49
D) 4x2 + 49
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 221) (-4x4 y-5 )(2x-1 y)
A) -2x
3
y4
Simplify the exponential expression. 222) (-3x)4
A) 81x
B) -8x
5
C) -8x
y6
3
y4
D) -8x3 y6
222) B) 81x4
C) -12x
D) -12x4
Evaluate the expression or indicate that the root is not a real number. 223) -81
A) 6561
B) 9
C) 9
D) Not a real number
81
223)
Find all numbers that must be excluded from the domain of the rational expression. x-9 224) 2 x + 13x + 36
A) x 9, x 4
221)
B) x 0
C) x -9, x -4
224) D) x 9
Factor completely, or state that the polynomial is prime. 225) 25x3 - 25x
225)
A) 25x(x2 - 1)
B) x(x + 5)(x - 5) D) 25x(x + 1)(x - 1)
C) 25x(x2 + 1) State the name of the property illustrated. 226) 8 + (-3) = (-3) + 8 A) Associative property of addition
226)
B) Identity property of addition C) Distributive property of multiplication over addition D) Commutative property of addition Perform the indicated computation. Write the answer in scientific notation. 227) (9 × 10-8)(2.1 × 10-7)
A) 1.89 × 1056
B) 189 × 10-15
C) 1.89 × 10-14
30
227) D) 18.9 × 10-14
Find the union of the two sets. 228) {2, 4, 9, 11} {2, 4, 13} A) {2, 4}
228) C) {2, 4, 9, 11, 13}
B)
D) {9, 11, 13}
List all numbers from the given set B that are members of the given Real Number subset. 229) B = {9, 7, -10, 0, 2 , 16, 0.6, 0.28} Rational numbers 3
A) 9, -10, 0, 2 , 16, 0.28, 0.6
B) 7, 2 , 0.28
C) 9, 0, 16
D) 7, 16
3
Simplify the exponential expression. 230) (x9 )-6
A) - x54
229)
3
230) B) 1
C) -6x9
x54
D) -6x54
Find all numbers that must be excluded from the domain of the rational expression. 231) 4 x-2
A) x -4
B) x 2
C) x 0
231) D) x -2
Simplify the exponential expression. 34
232)
232)
33
A) 3
B) 1
C) 4
3
D) 54
3
Determine whether the statement is true or false. 233) 23 > 14 A) True
233) B) False
Evaluate the expression without using a calculator. 234) 1001/2
A) 40
234)
B) 10
C) 5
D) 20
Multiply or divide as indicated. 2 235) (y - 11) ÷ 9y - 99 9 81
A) y - 11
235) 2
3
B) 9(y - 11)
C) (y - 11)
9y - 99
81
31
D)
1 y - 11
State the name of the property illustrated. 236) 8(-8 + 5) = -64 + 40 A) Commutative property of multiplication
236)
B) Associative property of multiplication C) Distributive property of multiplication over addition D) Associative property of addition Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 237) 31.6 and 2.5 237) A) |31.6 - 2.5| = 29.1 B) |-31.6 + 2.5| = -34.1
C) |2.5 - 31.6| = -29.1
D) |31.6 + 2.5| = 34.1
Multiply or divide as indicated. 2 2 238) x + 8x + 15 ÷ x + 5x x2 + 9x + 18 x2 + 10x + 24
A) x + 4 x
238) B)
x 2 x + 9x + 18
C) x + 4
Factor completely, or state that the polynomial is prime. 239) 6x4 - 96
D) x + 4
x2 + 6x
239)
A) 6(x2 + 4)(x2 - 4) C) 6(x2 + 4)(x + 2)(x - 2)
B) 6(x + 2)2 (x - 2)2 D) prime
Rationalize the denominator. 2 240) 11 + 3
A)
22 - 3 2 2
240) B)
22 - 3 2 14
C)
22 + 3 2 2
D) 3 22 + 11 33 2
Find the product.
241) (x + 3)(8x2 + 4x + 7) A) 8x3 + 24x2 + 12x + 21 C) 96x4 + 8x3 + 84x2 + 21
B) 32x3 + 16x2 + 28x D) 8x3 + 28x2 + 19x + 21
242) (2x + 9)(9x + 11) A) 18x2 + 103x + 99 C) 11x2 + 103x + 103
B) 18x2 + 103x + 103 D) 11x2 + 103x + 99
241)
242)
Add or subtract terms whenever possible. 243) -4 2 - 5 18 A) 19 2 B) -11 2
243) C) -19 2
32
D) -9 2
Add or subtract as indicated. 244) 2 + 9 x x-7
A) 14x - 11 x(x - 7)
Find the union of the two sets. 245) {9, 11, 12, 14} A) {9, 11, 12, 14}
244) B) 14x - 11
C) 11x - 14
x(7 - x)
x(x - 7)
D) 11x - 14 x(7 - x)
245) C) {12, 14}
B)
D) {9, 11}
Solve.
246) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.109x
246)
+ 87.16 approximates the apparent temperature for an actual temperature of 95°F, where x is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 10%? A) 95°F B) 88°F C) 97°F D) 87°F
Solve the problem. 247) Doctors use the rational expression DA A + 12
247)
to determine the dosage of a drug prescribed for children. In this expression, A = child's age and D = adult dosage. What is the difference in the child's dosage for a 12-year-old child and a 4-year-old child? Express the answer as a single rational expression in terms of D. A) 15 D B) 1 D C) 1 D D) 1 D 2 3 4 2
Perform the indicated operations. Write the resulting polynomial in standard form. 248) (6x6 + 4x4 - 9x) + (3x6 + 4x4 - 6x)
A) 9x6 + 8x4 - 15x C) -6x6 + 10x4 - 2x
248)
B) 2x11 D) 9x + 8x6 - 15x4
Determine whether the statement is true or false. 249) -30 < 0 A) True
249) B) False
Factor completely, or state that the polynomial is prime. 250) 2x2 - 16x - 18
A) (x + 1)(2x - 18)
250)
B) 2(x2 - 8x - 9)
Write the number in scientific notation. 251) 0.000576 A) 5.76 × 10-3 B) 5.76 × 10-4
C) (2x + 2)(x - 9)
D) 2(x + 1)(x - 9)
C) 5.76 × 10-5
D) 5.76 × 104
251)
33
Evaluate the expression without using a calculator. 252) 811/4
A) 36
252)
B) 243
C) 12
D) 3
Solve the problem. 253) Express the perimeter of the square as a single rational expression.
253)
9 x+4
A) 36
x+8
B)
36 x + 16
C)
9 x + 16
D) 36
x+4
Factor the trinomial, or state that the trinomial is prime. 254) 7x2 + 37x + 36
A) (7x + 9)(7x + 4) Perform the indicated operations. 255) (-4x2 y - xy) + (7x2 y + 6xy)
A) 11x2y + 7xy
254)
B) (7x + 4)(x + 9)
C) (7x + 9)(x + 4)
D) prime
B) 3x2 y + 7xy
C) 11x2y + 5xy
D) 3x2 y + 5xy
255)
Simplify the complex rational expression. 2 4+ x
256)
256)
x 1 + 4 8
A) x
16
B) 1
C) 16
Use the product rule to simplify the expression. 257) 72 A) 6 2 B) 12
258) 180x2 A) 180x
D) 16 x
257) C) 2 6
D) 8
C) 6 x 5
D) 5x2 6
258) B) 6 5x
Write the number in decimal notation without the use of exponents. 259) 2 × 103
A) 0.002
B) 20,000
C) 2000
34
259) D) 0.0002
Write the algebraic expression without parentheses. 260) -5(-4z) A) 20z B) -20z Simplify the algebraic expression. 261) (8z + 11) - (4z - 1) A) 4z + 12
260) C) 20 + z
D) 20 - 5z
261) B) 12z + 12
C) 4z + 10
D) 4z - 12
Simplify the radical expression. 3 262) x7 3
A) x2 x2
262) 3
3
C) x2 x
B) x x
3
D) x x2
Simplify the exponential expression. x12y11
263)
263)
x4 y2
A) x7 y9
B) x7 y8
C) x8 y9
D) xy9
3 10
264) 8x y
264)
4x2 y-7
A) 8xy17
B) 2x5 y17
C) 2xy3
D) 2xy17
B) degree 5
C) degree 8
D) degree 19
C) -9 6x
D) -38 6x
Find the degree of the polynomial. 265) 5x + 19x8 + 1
A) degree 9
265)
Add or subtract terms whenever possible. 266) 6x - 2 24x - 7 150x A) -38 180x B) -9 180x
266)
Simplify the complex rational expression. 1 1x
267)
7+
267)
1 x
A) 7x + 1 x-1
B) x + 1
C) x - 1
7x - 1
7x + 1
Factor completely, or state that the polynomial is prime. 268) 4b2 x - 81y - 81x+ 4b2 y
D) x - 1 7x
268)
A) (2bx - 9y)2
B) (2bx + 9y)(2bx - 9y) D) prime
C) (2b + 9)(2b - 9)(x + y)
35
List all numbers from the given set B that are members of the given Real Number subset.
269) B = {7, 7, -21, 0, 0.1, 4} Natural numbers A) 7, 0, 4
269) C) 7, 4
B) 7
D) 7, 0
Find the product.
270) (4x + 11)2 A) 4x2 + 121 C) 16x2 + 88x + 121
270) B) 4x2 + 88x + 121 D) 16x2 + 121
State the name of the property illustrated. 271) 1 · (6 · 14) = 1 · (14 · 6) A) Associative property of multiplication
271)
B) Distributive property of multiplication over addition C) Commutative property of multiplication D) Identity property of multiplication Simplify the exponential expression. Assume that variables represent nonzero real numbers. 23 272) (3x ) x15
A) 27
B) 27
x10
C) 3
x21
272)
D) 27
x9
x9
Multiply or divide as indicated. 2 2 273) x + 15x + 56 · x - 64 2 2 x + x - 56 x - x - 56
A) x + 7
273) B) x - 8
x-8
C) x + 8
x-7
x-7
Factor completely, or state that the polynomial is prime. 274) 10x5 - 10x
D) x - 8 x+7
274)
A) 10x(x2 + 1)(x + 1)(x - 1)
B) 10x(x4 + 1)(x2 + 1)(x + 1)(x - 1)
C) 10x(x2 + 1)(x2 - 1)
D) prime
Rationalize the denominator. 2 275) 7 - 10
A) 2 - 2 7
10
275) B) 14 + 2 10
C) 14 - 2 10
3
39
Write the number in scientific notation. 276) 36,000 A) 3.6 × 10-4 B) 3.6 × 103
D) 14 + 2 10 39
276) C) 3.6 × 10-3 36
D) 3.6 × 104
Evaluate the algebraic expression for the given value or values of the variable(s). 277) y - 5x ; x = -2 and y = 4 7x + xy
A) - 7
B) - 8
11
C) 3
11
277) D) 1
11
Simplify the exponential expression. 7 8 3 278) -9x y 3x11y-2 18
A) -27y
x12
278) B)
30
C) -27y
-27 12 x y30
x12
30
D) 27y
x12
Simplify using properties of exponents. 70x3/2
279)
279)
10x2/3
A) 7x5/4
B) 60x1/6
C) 7x5/6
D) 7x1/6
State the name of the property illustrated. 280) (3 + 4) + 8 = (4 + 3) + 8 A) Inverse property of addition
280)
B) Distributive property of multiplication over addition C) Commutative property of addition D) Associative property of addition Find the product. 281) (8x + 13)(8x - 13) A) 64x2 - 208x - 169
281) B) 64x2 - 169 D) x2 - 169
C) 64x2 + 208x - 169 Multiply or divide as indicated. 282) 4x + 8 ÷ 3x + 6 15 6
A) 2
15
282) B) 4x + 8
C) 8
45x
15
D) 7x + 14 21
Factor the trinomial, or state that the trinomial is prime. 283) x2 + 5x - 24
A) (x - 8)(x + 3)
283)
B) (x - 8)(x + 1)
C) (x + 8)(x - 3)
Factor out the greatest common factor. 284) x(5x + 4) + 2(5x + 4) A) (5x + 4)(x + 2) B) 2x(5x + 4)
D) prime
284) C) (5x + 4)(x - 2)
37
D) (5x + 2)(x + 4)
Determine whether the statement is true or false. 285) - A) False Simplify the exponential expression. 286) (3x-9 y4 z -3)-4 x36z 12
A)
81y16
285) B) True
286) B)
y8 81x13z 7
C)
y8 -12x 13z 7
36 12 D) x z
-12y-16
State the name of the property illustrated. 287) 8 · (17 · 7) = (17 · 7) · 8 A) Distributive property of multiplication over addition
287)
B) Associative property of multiplication C) Commutative property of multiplication D) Identity property of multiplication Factor the perfect square trinomial. 288) x2 - 14x + 49
A) (x + 7)2
288) C) (x - 7)2
B) (x - 7)(x + 7)
D) prime
Find the product.
289) (3 - 5x)2 A) 9x2 - 30x + 25 290) (x - 9)(x + 3) A) x2 - 6x - 27
289) B) 9 - 30x + 25x2
C) 9 + 25x2
D) 9 - 30x - 25x2 290)
B) x2 - 6x - 6
C) x2 - 27x - 6
D) x2 - 7x - 27
Multiply or divide as indicated. 291) 33x - 33 ÷ 11x - 11 10 30
A) 3(33x - 33) 11x - 11
291) B) 1
C) 363(x - 1)
B) 144 - y16
C) y8 - 144
9
300
2
D) 9
Find the product.
292) (12 - y4 )(12 + y4 ) A) 144 - y4
292) D) 144 - y8
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 293) -5 4
A) 20
C) 625
B) -625
38
D) -20
293)
Find the product.
294) (5x + 4)3 A) 25x6 + 20x3 + 4096 C) 125x3 + 300x2 + 240x + 64
294) B) 125x3 + 300x2 + 300x + 64 D) 25x2 + 40x + 16
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 295) -50 and -9 295) A) |-(-50) + (-9)| = 59 B) |(-9) + (-50)| = -59
C) |(-50) - (-9)| = 41
D) |(-9) - (-50)| = -41
Factor completely, or state that the polynomial is prime. 296) 4x2 - 4x - 24
A) 4(x - 2)(x + 3)
296)
B) prime
C) (4x + 8)(x - 3)
D) 4(x + 2)(x - 3)
State the name of the property illustrated. 297) 18 · (3 + 9) = 18 · 3 + 18 · 9 A) Commutative property of addition
297)
B) Associative property of multiplication C) Distributive property of multiplication over addition D) Commutative property of multiplication Find the product. 298) (7x + 4y)(7x - 4y) A) 49x2 + 56xy - 16y2
298) B) 7x2 - 4y2 D) 49x2 - 16y2
C) 49x2 - 56xy - 16y2 Simplify the exponential expression. 299) x10y0
A) x10
299) C) 1 x10
B) 1
Factor out the greatest common factor. 300) 3x - 27 A) 3(x - 9) B) 3x(x - 9)
D) 0
300) C) 3x(-9)
D) 3(x - 27)
Multiply or divide as indicated. 2 301) x - 24x + 144 ÷ 4x - 48 11x - 132 44 2
A) x - 24x + 144 (x - 12)2
301) 2
C) (x - 12)
B) 1
121
39
D) 44
Solve.
302) It is estimated that y, the number of items of a particular commodity (in millions) sold in the
302)
United States in year x, where x represents the number of years since 1990, is given by the formula y = 1.44x + 4.88. That is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold in 1997? A) 16.40 millions B) 44.24 millions C) 14.96 millions D) 4.88 millions
Solve the problem. 303) The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 36 months of age and a child 25 months of age? A) 17.4 inches B) 4.9 inches C) 43.1 inches D) 2.9 inches Simplify the complex rational expression. x +1 x+6
304)
304)
27 +1 2 x - 36
A) x - 6 x-3
B) 2x - 12
C) 2x - 12
x+3
x-3
Determine whether the statement is true or false. 305) 18 2 A) False
D) 2x + 12 x+3
305) B) True
Multiply or divide as indicated. 306) 1 ÷ 3 x + 2 x2 - 4
A)
3 x-2
Simplify the radical expression. 3 3 307) 10 · 25 3 A) 5 10
303)
306) B) x - 2
C) x + 2
3
3
D) x - 2
307) B)
6
3
250
C) 5 2
D)
3
250
Evaluate the expression or indicate that the root is not a real number. 308) 144 + 25 A) 13 B) 119 C) 169
D) 17
Write the number in scientific notation. 309) 7,781,440 A) 7.78144 × 107 B) 7.78144 × 106
D) 7.78144 × 10-6
308)
309) C) 7.78144 × 101
40
Simplify the exponential expression. x-6
310)
310)
x2
A) 1
x8
B) 1
D) 1
C) x8
x4
x12
Simplify the complex rational expression. 4 1 2 x -8 x - 4x - 32
311)
311)
1 +1 x+4
A) -1
B)
x
C) -
x2 - 5x - 40
x
x2 - 3x - 40
D) -
x2 - 4x - 32
Factor the trinomial, or state that the trinomial is prime. 312) x2 - x - 54
A) (x - 54)(x + 1)
312)
B) (x - 6)(x + 9)
C) (x + 6)(x - 9)
D) prime
Simplify the complex rational expression. 8 +1 x
313)
313)
8 -1 x
A) 8
B) x2 + 8
C)
x2 x2 + 8
D) 8 + x 8-x
Evaluate the expression for the given values of x and y. 314) |x| + |y| ; x = 5 and y = -3 x y
A) 2
314)
B) 0
C) 1
Determine whether the statement is true or false. 315) -13 15 A) True
B) False
Find the product. 316) (x - 7y)(x + 4y) A) x2 - 3xy - 28y2
B) x2 - 3xy - 3y2
C) x2 - 6xy - 28y2
D) x - 3xy - 28y
D) -1
315)
316)
Factor the trinomial, or state that the trinomial is prime. 317) x2 - x - 72
A) (x + 8)(x - 9)
x
317)
B) (x + 1)(x - 17)
C) (x + 9)(x - 8)
41
D) prime
Perform the indicated operations. 318) (11x4y2 - 9x2y2 + 12xy) + (5x4 y2 - 4x2 y2 + 2xy)
318)
A) 16x4y2 + 13x2 y2 + 14xy
B) 13x4y2 - 16x2 y2 + 14xy
C) -13x4 y2 + 16x2 y2 + 14xy
D) 16x4y2 - 13x2 y2 + 14xy
319) (4x2 y - 11xy + 12) + (-3x2 y + 5xy - 8) A) -x2 y - 16xy + 20 C) -6x3 y2 + 4
319) B) 7x2 y + 16xy + 20 D) x2 y - 6xy + 4
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 320) 25.7 and 33.2 320) A) -|25.7 + 33.2| = -58.9 B) |33.2 + 25.7| = 58.9
C) |33.2 - 25.7| = -7.5
D) |25.7 - 33.2| = 7.5
Find the product. 321) (x + 4y)(4x - 11y) A) x2 + 5xy + 5y2
B) 4x2 + 5xy - 44y2
C) 4x2 + 5xy + 5y2
D) x2 + 5xy - 44y2
321)
Factor completely, or state that the polynomial is prime. 322) x3 - 64x
A) x(x + 8)(x - 8)
322)
B) x(x - 8)2
C) (x2 + 8)(x - 8)
D) prime
Simplify the exponential expression. x 2
323)
323)
7
A) x 7
B) x
3
C) x
343
2
7
D) x
2
49
Factor using the formula for the sum or difference of two cubes. 324) x3 - 125
A) (x + 125)(x2 - 1)
B) (x - 5)(x2 + 5x + 25)
C) (x + 5)(x2 - 5x + 25)
D) prime
324)
Factor the trinomial, or state that the trinomial is prime. 325) x2 - 2xy - 15y2
A) (x + 5y)(x + y)
325)
B) (x - 5y)(x + 3y)
C) (x + 5y)(x + 3y)
42
D) prime
Multiply or divide as indicated. 2 2 326) x + 14x + 45 · x + 9x x2 + 18x + 81 x2 + 3x - 10
A)
1 x-2
326) B) x(x + 9)
C)
x-2
x x-2
D)
x 2 x + 18x + 81
Solve.
327) If a rock falls from a height of 100 meters above the ground, the height H (in meters) after x
327)
seconds can be approximated using the formula H = 100 - 4.9x2 . What is the height of the rock after 4 seconds? A) 1521.6 m B) 80.4 m C) -284.16 m D) 21.6 m
List all numbers from the given set B that are members of the given Real Number subset.
328) B = {16, 8, -13, 0, 0.9, 16} Integers A) 16, 0, 16 B) 16, 0
328) C) 16, -13, 0
Add or subtract terms whenever possible. 3 3 329) 8 24 + 81 3 3 A) 11 3 B) 8 105
D) 16, -13, 0, 16
329) 3
C) 19 3
Determine whether the statement is true or false. 330) < 3 A) False
3
D) 9 105
330) B) True
Evaluate the expression or indicate that the root is not a real number. 331) (-3)2
A) 9 C) 3
331)
B) -3 D) Not a real number
Solve the problem.
332) The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d
332)
miles. Use a calculator to determine the duration of a storm with a diameter of 15 miles. Round to the nearest hundredth. A) 0.27 hours B) 1.08 hours C) 58.09 hours D) 4.07 hours
Simplify the exponential expression. 333) (x-5 )7
A) -x35
333) C) 1 x35
B) -5x7
43
D) -5x35
Factor completely, or state that the polynomial is prime. 334) 4x3 - 4
334)
A) 4(x3 - 1)
B) 4(x - 1)(x2 + x + 1)
C) 4(x + 1)(x2 - x + 1)
D) prime
Simplify the exponential expression. x5 y-7
335)
335)
z -8 5 7
5 8
A) x z
7 C) y
B) x z
y8
y7
8 D) z
x5 z8
x5 y7
Write the number in decimal notation without the use of exponents. 336) 7.34 × 10-4
A) -734,000
336)
B) 0.0000734
C) 0.000734
D) 0.00734
B) degree 13
C) degree 20
D) degree 5
Find the degree of the polynomial. 337) x5 - 7x4 y9 + 8xy - 6x + 2
A) degree -7
337)
List all numbers from the given set B that are members of the given Real Number subset. 338) B = {15, 5, 0, 7 , 9, -0.3, 0.79, -24} Real numbers 8
A) 15, 5, 0, 7 , 9, -0.3, 0.79, -24
B) 15, 5, 7 , 9, -0.3, 0.79, -24
C) 15, 5, 0, 7 , 9, 0.79
D) 15, 0, 7 , -0.3, 0.79, -24
8
8
8
8
Perform the indicated computation. Write the answer in scientific notation. 339) 0.00016 × 0.0003 0.0008
A) 6 × 105
338)
C) 48 × 106
B) 6 × 10-5
Rewrite the expression without absolute value bars. 340) |3 + (-11)| A) -14 B) 8
339) D) 48 × 10-6
340) C) -8
44
D) 14
Provide an appropriate response.
341) The rational expression 120x describes the cost, in millions of dollars, to inoculate x percent of 100-x
341)
the current population of cattle against a particular virus. Choose which of the following statements are true with regard to this mathematical model. I. The expression will be undefined when x = 100. II. The cost of inoculating 90 percent of cattle is 900 million dollars more than the cost of inoculating 60 percent of cattle. III. This expression will calculate inoculation costs for any population of cattle, no matter what the size. A) Only II and III are true. B) Only I and III are true.
C) All three statements are true.
D) Only I and II are true.
Find the product. 342) (5x2 + 8x)(5x2 - 8x)
342)
A) 10x4 - 16x2
B) 25x4 - 64x2
C) 25x4 - 80x3 - 64x2
D) 25x4 + 80x3 - 64x2
343) (4xy - 3)(8xy + 7) A) 12x2y2 + 4xy + 4 C) 32x2y2 + 4xy - 21
343) B) 32x2y2 + 4xy + 4 D) 12x2y2 + 4xy - 21
344) (7x3 - 6)(x2 - 2) A) 7x5 - 20x2 + 12 C) 7x5 - 14x3 - 6x2 + 12
344) B) 7x6 - 14x3 - 6x2 + 12 D) 7x5 - 20x3 + 12
Simplify the exponential expression. 345) 100
A) -1 346) (11x5)2 A) 11x7
345) B) 0
C) 10
D) 1 346)
B) 121x10
C) 11x10
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 347) 4x + 7 + 2x2
A) Yes; 2x2 + 4x + 7
B) No
Determine whether the statement is true or false. 348) 18 13 A) True
B) False
D) 121x5
347)
348)
45
Use the product rule to simplify the expression. 349) 6 A) 6 B) 3 2
349) D) 2 3
C) 2
Find the product.
350) (x + 11)(x2 + 5x - 7) A) x3 + 16x2 + 62x - 77 C) x4 + 11x3 + 5x2 + 48x - 77
350) B) x3 + 16x2 + 62x + 77 D) x3 + 16x2 + 48x - 77
Factor the trinomial, or state that the trinomial is prime. 351) 20x2 - 27x + 9
A) (20x + 3)(x + 3) Simplify the exponential expression. 352) 33 · 3 -4
A) 2187
351)
B) (5x - 3)(4x - 3)
C) (5x + 3)(4x + 3)
B) - 1 3
C) 1 3
352) D) -3
Factor by grouping. Assume any variable exponents represent whole numbers. 353) x3 - 4x2 - 2x + 8
A) (x + 4)(x2 + 2)
D) prime
B) (x - 2)(x2 - 4)
C) (x - 4)(x - 2)
353) D) (x - 4)(x2 - 2)
Simplify the exponential expression. Assume that variables represent nonzero real numbers. -5 -3 4 -1 354) 12x y z 3xy-3 z -4
A) x
6
B) x
4z 8
4
6 6
C) x y
4z 8
4z 8
354)
D) 4x
6
z8
Rationalize the denominator. 2 355) 5 - 10
A) 2 - 2 5
10
355) B) 10 - 2 10
C) 10 + 2 10
15
5
Evaluate the algebraic expression for the given value or values of the variable(s). 356) 6x + 7; x=3 A) 36 B) 25 C) 11
46
D) 10 + 2 10 15
356) D) 13
State the name of the property illustrated. 357) 4(x + 7) = 4x + 4 · 7 A) Commutative property of multiplication
357)
B) Identity property of multiplication C) Associative property of multiplication D) Distributive property of multiplication over addition Evaluate the expression or indicate that the root is not a real number. 358) 144 + 25 A) 13 B) 119 C) 169
358) D) 17
Add or subtract as indicated. 359) 11 + 22 x-9 9-x
A) - 11
359) B) 11
x-9
C) 33
x-9
x-9
D) - 33
x-9
Find all numbers that must be excluded from the domain of the rational expression. 360) x + 8 x2 - 81
A) x 9, x -9
B) x -8
C) x 81
360) D) x 9
Rewrite the expression without absolute value bars. 361) -16 1
A) -16
361) C) 1
B) -1
D) 16
Add or subtract as indicated. 2 2 362) x - 2x + x + x x2 + 7x x2 + 7x
A) 2x + 1
B) x - 1
x+7
363) 4x + 5 x+1
x-1
362) C) 2x - 1
x+7
x+7
D) -1
x+7
8 2 x -1
A) 4x
x-1
Simplify the exponential expression. 364) (32 )4 A) 6561
363) B) 4x - 3
C) 4x - 3
D) x + 1
B) 36
C) 24
D) 729
x+1
x-1
x-1
364)
47
Add or subtract terms whenever possible. 3 3 365) y 128x - 16xy3 3
365)
3
3
A) 4y 2x - 128 2xy3
B) y -14xy3
3
3
C) 2y 2x
D) (y + 1) 18
Simplify the exponential expression. 366) (5x)2
A) 10x2
366) B) 10x
C) 25x
D) 25x2
Add or subtract as indicated. 5 367) x x2 - 16 x 2 + 5x + 4
367)
A)
x2 - 4x + 20 (x - 4)(x + 4)(x + 1)
B) x - 4x + 20
2
C)
x2 - 4 (x - 4)(x + 4)(x + 1)
D)
(x - 4)(x + 4) x2 + 4x + 20 (x - 4)(x + 4)(x + 1)
Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places. 368) In a state with a population of 2,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state? A) $12 × 1011 B) $12 × 1010 C) $1.2 × 109 D) $1.2 × 1010 Rationalize the denominator. 369) 144 7
A) 12 7
369) B) 144 7
D) 12 7
C) 61
7
7
Simplify the exponential expression. 3x3 y2 4
370)
370)
z3
12 8 A) 3x y z 12
368)
7 6
12 8 C) 3x y
B) 81x y z7
z7
12 8 D) 81x y z 12
Find the product.
371) (x2 y2 + 7)2 A) x2 y2 + 14xy + 49 C) x4 y4 + 7x2 y2 + 49
371) B) x4 y4 + 49 D) x4 y4 + 14x2 y2 + 49
48
List all numbers from the given set B that are members of the given Real Number subset.
372) B = {3, 5, -19, 0, 0.1, 16} Whole numbers A) 3, 0, 16 B) 3, 0
372) C) 3, -19, 0, 16
D) 3, -19, 0
C) (3x + 4)(5x - 2)
D) prime
Factor the trinomial, or state that the trinomial is prime. 373) 15x2 + 14x - 8
A) (15x + 4)(x - 2)
373)
B) (3x - 4)(5x + 2)
Find all numbers that must be excluded from the domain of the rational expression. x+3 374) x2 - 7x + 12
A) x 4, x 3 Find the product. 375) (5 + 9x)(5 - 9x) A) 25 - 81x2 Simplify the exponential expression. 376) x-5 · x2
A) -x3
374)
B) x -4, x -3
C) x -3
D) x 0
B) 25 + 90x - 81x2
C) 25 - 90x - 81x2
D) 81x2 - 25
C) x3
D) 1 x3
C) -25
D) 1 10
375)
376) B) - 1 x3
377) -5 -2
377)
A) - 1 25
B) 25
Simplify the complex rational expression. 3 1x
378)
1+
378)
3 x
A) x + 3 x-3
B) x - 3
C) x + 3
x+3
D) x - 3
Simplify the exponential expression. Assume that variables represent nonzero real numbers. 379) (-7)3
A) -21
C) 343
B) -343
Write the number in decimal notation without the use of exponents. 380) 2.714 × 10-6
A) -2,714,000
B) 0.000002714
C) 0.00002714
49
379)
D) 21
380) D) 0.0000002714
Simplify the complex rational expression. 10 - 10 5x - 1
381)
381)
10 + 10 5x - 1
A) 2 + 5x 5x
B) 2 - 5x
C)
5x
5x 2 - 5x
D) 2 - x x
Factor the trinomial, or state that the trinomial is prime. 382) 7x2 - 23x - 20
A) (7x - 5)(x + 4)
382)
B) (7x - 4)(x + 5)
C) (7x + 5)(x - 4)
D) prime
Find the product.
383) (x - 2)3 A) x3 - 6x2 + 8x - 8 C) x3 - 2x2 + 8x - 8
383) B) x3 - 6x2 + 12x - 8 D) x3 - 6x2 + 6x - 8
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. 384) 70 and 89 384) A) |70 + 89| = 159 B) -|89 - 70| = -19
C) -|70 + 89| = -159
D) |70 - 89| = 19
Use the quotient rule to simplify the expression. 56x4
385)
385)
2x
A) 2 x 7x
B) 2 x x
2 56 2
C) 56x3
D) x
C) (7x + 5)(x - 3)
D) prime
Factor the trinomial, or state that the trinomial is prime. 386) 7x2 + 32x + 15
A) (7x - 3)(x + 5)
386)
B) (7x + 3)(x - 5)
Find the product.
387) (7x + 9y)2 A) 49x2 + 81y2 C) 7x2 + 126xy + 81y2
Simplify the algebraic expression. 388) -5(2x - 9) - 4x + 7 A) -14x + 52
387) B) 49x2 + 126xy + 81y2 D) 7x2 + 81y2
388) B) 14x + 52
C) 6x + 52
50
D) -14x - 38
Add or subtract as indicated. 389) 3x + 1 + 3x + 7 3x + 4 3x + 4
A) 2
389) B) 4x + 5
C)
3x + 4
Write the number in scientific notation. 390) 52,000,000 A) 5.2 × 107 B) 5.2 × 10-6 Find the intersection of the two sets. 391) {1, 7, 5, 8} {5, 11, 1} A) {1, 5}
2 3x + 4
D) 1
390) C) 5.2 × 10-7
D) 5.2 × 106
391) B) {1}
C)
Simplify using properties of exponents. 392) (81x8y4 )1/2 A) 9 x4 y2 B) 81x4y2 2
D) {1, 5, 8, 7, 11}
392) C) 9x4 y2
D) 6561x16y4
Factor using the formula for the sum or difference of two cubes. 393) 8x3 + 1
393)
Factor and simplify the algebraic expression. 394) (x + 7)1/4 + (x + 7)3/4
394)
A) (2x - 1)(4x2 + 1) C) (2x - 1)(4x2 + 2x + 1)
B) (2x + 1)(4x2 - 2x + 1) D) prime
A) (x + 7)1/2 (1 + (x + 7)3/2) C) (x + 7)1/2 (1 + (x + 7)1/4)
Simplify the exponential expression. 395) (9x7 )(-8x5 )
A) 72x12
B) (x + 7)1/2 ((x + 7)1/2 + 1) D) (x + 7)1/4 (1 + (x + 7)1/2)
395) B) -72x35
C) -72x12
D) 72x35
Evaluate the algebraic expression for the given value or values of the variable(s). 396) 5 + 4(x - 2)3 ; x=4
A) -27
B) 37
C) 13
396) D) 72
Simplify the exponential expression. x10
397)
397)
x4
A) x14
B) x6
C) x-2
51
D) 1
x6
Solve.
398) The winning times (in seconds) in a speed-skating event for men can be represented by the
398)
formula T = 46.36 - 0.091x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1990? Round to the nearest hundredth. A) 3238.83 sec B) 40.90 sec C) 41.81 sec D) 39.99 sec
Write the number in decimal notation without the use of exponents. 399) 1.19 × 107
A) 11,900,000
B) 83.3
399)
C) 1,190,000
D) 119,000,000
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 400) x2 - x3 + x4 - 9
A) Yes; x4 - x3 + x2 - 9
Find the product. 401) (1 + x4 )(1 - x4 )
A) 2 - x8
402) (2x + 1)(x - 8) A) 2x2 - 16x - 8
400)
B) No
401) B) 1 - x8
C) 1 - x16
D) 2 - x16
B) x2 - 15x - 16
C) x2 - 8x - 15
D) 2x2 - 15x - 8
402)
Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. 8x2 - 49x + 6
403)
403)
x-6
A) 8x2 - 50, no restrictions on x C)
B) 8x - 1, x 6 2
D) 8x - 49x + 6 , x 6
1 ,x 6 x-6
x-6
Rewrite the expression without absolute value bars. 404) -4 - -5 A) 1 B) 9
404) C) -9
D) -1
Find the product.
405) (7x - 1)(x2 - 5x + 1) A) 7x3 - 36x2 + 12x - 1 C) 7x3 - 35x2 + 7x + 1
405) B) 7x3 + 36x2 - 12x + 1 D) 7x3 - 34x2 + 2x - 1
52
Factor using the formula for the sum or difference of two cubes. 406) 64x3 - 1
A) (4x - 1)(16x2 + 1)
B) (4x - 1)(16x2 + 4x + 1)
C) (4x + 1)(16x2 - 4x + 1)
D) prime
406)
Simplify the exponential expression. 2x8
407)
407)
x5
A) 2x13 408) (-6x5 y6 )2 A) -36x10y12
B) 8x3
C) 2x3
D) 6x 408)
B) 36x10y12
C) 36x7y8
Factor using the formula for the sum or difference of two cubes. 409) x3 + 125
A) (x - 5)(x2 + 5x + 25) C) (x + 5)(x2 - 5x + 25)
D) -6x10y12
409)
B) (x + 5)(x2 + 25) D) prime
Add or subtract terms whenever possible. 410) 9 + 72 + 64 + 98 A) 13 2 + 9 + 64
410) B) 85 2 + 11 D) 13 2 + 11
C) 72 + 98 + 11
53
Answer Key Testname: CH 0
1) B 2) A 3) A 4) B 5) A 6) D 7) C 8) A 9) C 10) D 11) A 12) D 13) A 14) D 15) B 16) D 17) C 18) D 19) C 20) B 21) D 22) C 23) C 24) A 25) C 26) C 27) D 28) B 29) B 30) D 31) A 32) B 33) C 34) B 35) D 36) A 37) C 38) B 39) B 40) A 41) A 42) B 54
Answer Key Testname: CH 0
43) D 44) B 45) B 46) D 47) C 48) D 49) D 50) D 51) D 52) A 53) A 54) C 55) A 56) A 57) D 58) B 59) C 60) A 61) B 62) B 63) D 64) B 65) A 66) C 67) B 68) C 69) A 70) A 71) B 72) D 73) C 74) A 75) B 76) C 77) B 78) C 79) D 80) D 81) C 82) C 83) D 84) C 55
Answer Key Testname: CH 0
85) D 86) D 87) C 88) A 89) A 90) B 91) B 92) D 93) B 94) B 95) B 96) C 97) B 98) C 99) A 100) B 101) B 102) B 103) D 104) C 105) C 106) D 107) B 108) A 109) C 110) D 111) B 112) D 113) D 114) A 115) B 116) A 117) C 118) A 119) A 120) C 121) B 122) D 123) B 124) B 125) C 126) B 56
Answer Key Testname: CH 0
127) D 128) A 129) D 130) C 131) A 132) B 133) D 134) D 135) D 136) A 137) B 138) D 139) C 140) A 141) C 142) C 143) C 144) A 145) B 146) A 147) A 148) D 149) D 150) D 151) B 152) A 153) D 154) C 155) A 156) B 157) A 158) B 159) B 160) A 161) C 162) A 163) B 164) C 165) C 166) B 167) D 168) D 57
Answer Key Testname: CH 0
169) D 170) A 171) B 172) A 173) D 174) B 175) A 176) B 177) C 178) D 179) A 180) C 181) B 182) A 183) B 184) C 185) C 186) D 187) B 188) D 189) D 190) B 191) C 192) C 193) B 194) B 195) D 196) C 197) C 198) C 199) B 200) B 201) C 202) B 203) C 204) B 205) A 206) B 207) D 208) C 209) C 210) D 58
Answer Key Testname: CH 0
211) D 212) D 213) B 214) A 215) B 216) D 217) A 218) D 219) A 220) A 221) C 222) B 223) D 224) C 225) D 226) D 227) C 228) C 229) A 230) B 231) B 232) A 233) A 234) B 235) A 236) C 237) A 238) A 239) C 240) A 241) D 242) A 243) C 244) C 245) A 246) B 247) C 248) A 249) A 250) D 251) B 252) D 59
Answer Key Testname: CH 0
253) D 254) C 255) D 256) D 257) A 258) C 259) C 260) A 261) A 262) C 263) C 264) D 265) C 266) D 267) C 268) C 269) C 270) C 271) C 272) D 273) C 274) A 275) D 276) D 277) A 278) C 279) C 280) C 281) B 282) C 283) C 284) A 285) B 286) A 287) C 288) C 289) B 290) A 291) D 292) D 293) B 294) C 60
Answer Key Testname: CH 0
295) C 296) D 297) C 298) D 299) A 300) A 301) B 302) C 303) D 304) C 305) B 306) B 307) C 308) A 309) B 310) A 311) C 312) D 313) D 314) B 315) A 316) A 317) A 318) D 319) D 320) D 321) B 322) A 323) D 324) B 325) B 326) C 327) D 328) D 329) C 330) A 331) C 332) D 333) C 334) B 335) B 336) C 61
Answer Key Testname: CH 0
337) B 338) A 339) B 340) B 341) D 342) B 343) C 344) C 345) D 346) B 347) A 348) B 349) A 350) D 351) B 352) C 353) D 354) A 355) D 356) B 357) D 358) D 359) A 360) A 361) A 362) C 363) C 364) A 365) C 366) D 367) A 368) D 369) D 370) D 371) D 372) A 373) C 374) A 375) A 376) D 377) A 378) B 62
Answer Key Testname: CH 0
379) B 380) B 381) B 382) C 383) B 384) D 385) A 386) D 387) B 388) A 389) A 390) A 391) A 392) C 393) B 394) D 395) C 396) B 397) B 398) D 399) A 400) A 401) B 402) D 403) B 404) A 405) A 406) B 407) C 408) B 409) C 410) D
63
Chapter 1 Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the correct viewing rectangle dimensions with the figure.
1)
1)
A) [-16, 16, 4] by [-4, 4, 2] C) [-4, 4, 2] by [-4, 4, 2]
B) [-20, 20, 2] by [-20, 20, 2] D) [-4, 4, 2] by [-80, 80, 8]
Match the graph with its function using the x-intercepts.
2)
2)
A) y = x4 - 25x2 + 12 C) y = x4 + 25x2 + 144
B) y = x4 + 25x2 - 12 D) y = x4 - 25x2 + 144
1
Match the correct viewing rectangle dimensions with the figure.
3)
3)
A) [-1, 8, 1] by [-4, 5, 1] C) [-1, 8, 1] by [-1, 8, 1]
B) [-10, 5, 1] by [-10, 5, 1] D) [-4, 5, 1] by [-1, 8, 1]
4)
4)
A) [-25, 25, 5] by [-25, 25, 5] C) [-25, 25, 10] by [-25, 25, 10]
B) [-50, 25, 5] by [-50, 25, 5] D) [-5, 5, 5] by [-5, 5, 5]
2
Match the story with the correct figure. 5) The height of an animal as a function of time.
5)
A)
B)
C)
D)
6) Mark started out by walking up a hill for 5 minutes. For the next 5 minutes he walked down a
steep hill to an elevation lower than his starting point. For the next 10 minutes he walked on level ground. For the next 10 minutes he walked uphill. Determine which graph of elevation above sea level versus time illustrates the story.
A)
3
6)
B)
C)
D)
4
Match the graph with its function using the x-intercepts.
7)
7)
A) y = x-2 - x-1 - 2 C) y = x-2 - x-1 + 2
B) y = x-2 + x-1 - 2 D) y = x-2 + x-1 + 2
8)
8)
A) y = 6x-2 + 5x-1 - 1 C) y = 6x-2 - 5x-1 + 1
B) y = 6x-2 - 5x-1 - 1 D) y = 6x-2 + 5x-1 + 1
5
9)
9)
A) y = x1/2 - 15x1/4 - 16 C) y = x1/2 + 15x1/4 - 16
B) y = x1/2 + 2x1/4 - 1 D) y = x1/2 + 2x1/4 + 1
10)
10)
A) y = 2(x - 3)2 + 3(x - 3) - 5 C) y = 2(x + 3)2 + 3(x + 3) - 5
B) y = 2(x + 3)2 - 3(x + 3) - 5 D) y = 2(x - 3)2 - 3(x - 3) - 5
6
11)
11)
A) y = (x + 2)2 - 9(x + 2) + 18 C) y = (x + 2)2 - 5(x + 2) + 4
B) y = (x + 2)2 + 9(x + 2) + 18 D) y = (x + 2)2 + 5(x + 2) + 4
Match the story with the correct figure. 12) The amount of rainfall as a function of time, if the rain fell more and more softly.
A)
B)
C)
D)
7
12)
Chapter 3 Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. 1) f(x) = -2x2 - 3x - 3 1)
A) falls to the left and rises to the right
B) rises to the left and rises to the right
C) rises to the left and falls to the right
D) falls to the left and falls to the right
1
Solve.
2) The profits (in millions) for a company for 8 years were as follows:
2)
Year, x Profits, P 1993, 1 1.1 1994, 2 1.7 1995, 3 2.0 1996, 4 1.4 1997, 5 1.3 1998, 6 1.5 1999, 7 1.8 2000, 8 2.1 Which of the following polynomials is the best model for this data? A) P(x) = -0.03x4 - 0.3x2 + 1.3x + 0.17 B) P(x) = 0.05x2 - 0.8x + 6
C) P(x) = 0.03x3 - 0.3x2 + 1.3x + 0.17
D) P(x) = -0.08x3 + 7x2 + 1.3x - 0.18
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. 3) f(x) = 3x2 - 2x + 1 3)
A) rises to the left and rises to the right
B) falls to the left and falls to the right
C) rises to the left and falls to the right
D) falls to the left and rises to the right
2
4) f(x) = -4x3 - 2x2 + 2x + 2 A) falls to the left and falls to the right
B) rises to the left and rises to the right
C) rises to the left and falls to the right
D) falls to the left and rises to the right
4)
3
5) f(x) = 4x4 - 2x2 A) falls to the left and rises to the right
B) rises to the left and falls to the right
C) falls to the left and falls to the right
D) rises to the left and rises to the right
5)
4
6) f(x) = 4x3 - 3x2 - 2x - 2 A) falls to the left and rises to the right
B) rises to the left and rises to the right
C) rises to the left and falls to the right
D) falls to the left and falls to the right
6)
5
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Complete the following: (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. (c) Find the y-intercept. (d) Graph the function. 7) f(x) = x2 (x + 2) 7)
8) f(x) = -2(x - 3)(x + 2)3
8)
6
9) f(x) = (x + 2)(x - 1)2
9)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 10) f(x) = 2x2 - 2x + 2 10)
A) minimum; 3 , 1
B) maximum; 3 , 1
C) maximum; 1 , 3
D) minimum; 1 , 3
2 2
2 2
2 2
2 2
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 11) f(x) = x2 - 2x - 4
A) (-2, 4)
B) (1, -5)
C) (-1, -1)
7
D) (1, -7)
11)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 12) x3 + 3x2 - x - 3 > 0 12)
A) (- , - 3) (-1, 1)
B) (- , - 1) (1, 3)
C) (-1, 1) (3, )
D) (- 3, -1) (1, )
Determine whether the function is a polynomial function. 2 13) f(x) = x3 - x2 - 2 A) Yes
13) B) No
Determine whether the graph shown is the graph of a polynomial function.
14)
14)
A) polynomial function
B) not a polynomial function
Find the vertical asymptotes, if any, of the graph of the rational function. 15) g(x) = x x2 - 25
A) x = 5, x = -5, x = 0 C) x = 5
B) x = 5, x = -5 D) no vertical asymptote
8
15)
Solve the problem. 16) y varies directly as x and inversely as the square of z. y = 72 when x = 72 and z = 3. Find y when x = 43 and z = 10. A) 38.7 B) 3.87 C) 12.9 D) 477.78 Determine whether the function is a polynomial function. 2 17) f(x) = x - 8 x5
17)
A) Yes
B) No
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 18) f(x) = x3 + x2 - 4
A) origin symmetry
16)
B) y-axis symmetry
18)
C) neither
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 19) f(x) = 7x3 - 6x2 + x + 3.5 19)
A) 2 or 0 positive zeros, 1 negative zero B) 3 or 1 positive zeros, 2 or 0 negative zeros C) 3 or 1 positive zeros, 1 negative zero D) 2 or 0 positive zeros, no negative zeros Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 20) f(x) = 7x2 - x3 20)
B) 0, touches the x-axis and turns around;
A) 0, touches the x-axis and turns around;
7, crosses the x-axis
7, crosses the x-axis; - 7, crosses the x-axis C) 0, touches the x-axis and turns around; 7, touches the x-axis and turns around
D) 0, crosses the x-axis; 7, crosses the x-axis; - 7, crosses the x-axis
Divide using synthetic division. -2x3 - 10x2 - 5x + 12
21)
21)
x+4
A) -2x2 - 2x + 3
B) -2x2 x - 5 + 3
C) 2x2 - 4x + 3
D) - 1 x2 - 5 x - 5
2
2
2
4
Find the indicated intercept(s) of the graph of the function. 22) y-intercept of f(x) = x - 3 x2 + 3x - 2
A) 0, 3 2
22)
B) 0, - 2
C) (0, 3)
3
9
D) none
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 23) f(x) = 6x4 - 3x3 + 4x - 3; between -1 and 0 23)
A) f(-1) = -2 and f(0) = -3; no C) f(-1) = 2 and f(0) = 3; no
B) f(-1) = -2 and f(0) = 3; yes D) f(-1) = 2 and f(0) = -3; yes
Solve the problem. 24) The amount of simple interest earned on an investment over a fixed amount of time is jointly proportional to the principle invested and the interest rate. A principle investment of $3200.00 with an interest rate of 5% earned $320.00 in simple interest. Find the amount of simple interest earned if the principle is $1800.00 and the interest rate is 2%. A) $7200.00 B) $128.00 C) $180.00 D) $72.00
25) If y varies directly as x, and y = 2 when x = 4, find y when x = 32. A) 64
C) 1 4
B) 4
24)
25) D) 16
Find the axis of symmetry of the parabola defined by the given quadratic function. 26) f(x) = (x + 1)2 - 6
26)
A) x = -6
B) x = 1
C) x = 6
D) x = -1
27) f(x) = 7 - (x + 4)2 A) x = 4
B) x = 7
C) x = -7
D) x = -4
27)
Solve the problem. 28) Among all pairs of numbers whose sum is 42, find a pair whose product is as large as possible. A) 10.5 and 10.5 B) 21 and 21 C) 41 and 1 D) 23 and 19 Graph the polynomial function. 29) f(x) = x4 - 4x2
28)
29)
10
A)
B)
C)
D)
Use synthetic division and the Remainder Theorem to find the indicated function value. 30) f(x) = x5 - 9x4 + 4x3 + 2; f(-3)
A) -1078
B) 1078
C) -835
If y varies inversely as x, find the inverse variation equation for the situation. 31) y = 0.2 when x = 0.4 A) y = 12.5 B) y = 12.5x C) y = 0.08 x x Use the vertex and intercepts to sketch the graph of the quadratic function. 32) f(x) = 2x2 - 8x + 2
11
30) D) -118
31) D) y = 0.5x
32)
A)
B)
C)
D)
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 33) f(x) = 3 - x2 - 2x
A) (1, 4)
B) (1, - 4)
C) (- 1, - 4)
33)
D) (- 1, 4)
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 34) f(x) = x3 + x2 - 12x 34)
A) 0, multiplicity 1, touches the x-axis and turns around;
- 4, multiplicity 1, touches the x-axis and turns around; 3, multiplicity 1, touches the x-axis and turns around B) - 4, multiplicity 2, touches the x-axis and turns around 3, multiplicity 1, crosses the x-axis C) 0, multiplicity 1, crosses the x-axis 4, multiplicity 1, crosses the x-axis -3, multiplicity 1, crosses the x-axis D) 0, multiplicity 1, crosses the x-axis - 4, multiplicity 1, crosses the x-axis 3, multiplicity 1, crosses the x-axis
Graph the rational function.
12
35) f(x) =
x2
35)
x2 - x - 56
A)
B)
C)
D)
13
Solve the problem. 36) A number minus the product of 16 and its reciprocal is less than zero. Find the numbers which satisfy this condition. A) any number between -4 and 4
36)
B) any number between 0 and 4 C) any number less than 4 D) any number less than -4 or between 0 and 4 Use transformations of f(x) =
37) f(x) =
1 1 or f(x) = to graph the rational function. x x2
1
37)
(x - 5)2
A)
B)
14
C)
D)
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 38) 2x4 - 13x3 + 49x2 - 77x + 39 = 0 38)
A) {-1, 3 , 2 + 3i, 2 - 3i}
B) {-1, - 3 , 3 + 2i, 3 - 2i}
C) {1, - 3 , 3 + 2i, 3 - 2i}
D) {1, 3 , 2 + 3i, 2 -3i}
2
2
2
2
Graph the polynomial function. 39) f(x) = x3 - 2x2 - 5x + 6
39)
A)
B)
15
C)
D)
Find the x-intercepts (if any) for the graph of the quadratic function. 40) f(x) = (x + 1)2 - 1
A) (2, 0) and (-2, 0) C) (0, 0) and (2, 0)
B) (0, 0) and (-2, 0) D) (0, 0) and (-1, 0)
16
40)
Graph the polynomial function. 41) f(x) = x(x - 2)(x - 1)
41)
A)
B)
C)
D)
Find the x-intercepts (if any) for the graph of the quadratic function. 42) f(x) = 6 + 5x + x2
A) (3, 0) and (-2, 0) C) (-3, 0) and (-2, 0)
42)
B) (-3, 0) and (2, 0) D) (3, 0) and (2, 0)
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 43) f(x) = x5 - 6x2 + 4x + 21
A) ± 1, ± 7, ± 3
B) ± 1, ± 7, ± 3, ± 21
C) ± 1, ± 1 , ± 1 , ± 1 7
3
D) ± 1, ± 1 , ± 1 , ± 1 , ± 7, ± 3, ± 21
21
7
17
3
21
43)
Solve the problem. 44) You drive 120 miles along a scenic highway and then take a 22-mile bike ride. Your driving rate is 4 times your cycling rate. Suppose you have no more than a total of 5 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Use a rational inequality to determine the possible values of x. A) x 25.1 mph B) x 63.5 mph C) x 10.4 mph D) x 10.4 mph
44)
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 45) f(x) = x2 + 2x - 1 45)
A) minimum; - 2, - 1 C) maximum; - 2, - 1
B) minimum; - 1, - 2 D) maximum; - 1, - 2
Determine the maximum possible number of turning points for the graph of the function. 46) f(x) = (x + 1)(x - 2)(x - 7)(x - 4) A) 1 B) 3 C) 0 D) 4
46)
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
47)
47)
A) y-axis symmetry
B) origin symmetry
C) neither
Find the y-intercept of the polynomial function. 48) f(x) = -x2(x + 2)(x - 8)
A) -16
48)
B) 16
C) 0
D) -8
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 49) f(x) = (x + 2)2 + 2
A) (-2, -2)
B) (0, 2)
C) (-2, 2)
D) (2, 0)
Solve the problem. 50) The owner of a video store has determined that the profits P of the store are approximately given by P(x) = -x2 + 50x + 67, where x is the number of videos rented daily. Find the maximum profit to the nearest dollar. A) $1250
B) $1317
C) $692
18
49)
D) $625
50)
Find an nth degree polynomial function with real coefficients satisfying the given conditions. 51) n = 3; -1 and 3 + 2i are zeros; leading coefficient is 1 A) f(x) = x3 - 5x2 + 7x + 13 B) f(x) = x3 + 5x2 + 7x - 14
C) f(x) = x3 - 5x2 + 15x + 13
51)
D) f(x) = x3 - 4x2 + 7x + 13
Solve the problem. 52) A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 648 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. A) 108 ft by 162 ft B) 162 ft by 162 ft C) 81 ft by 162 ft D) 54 ft by 243 ft
52)
Solve.
53) Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function increasing? A) 0 through 10 and 30 through 50
53)
B) 0 through 10 and 40 through 50 D) 0 through 50
C) 0 through 20 and 30 through 50
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. 54) Crosses the x-axis at -1, 0, and 4; lies below the x-axis between -1 and 0; lies above the x-axis 54) between 0 and 4. A) f(x) = x3 + 3x2 - 4x B) f(x) = -x3 + 3x2 + 4x
C) f(x) = - x3 - 3x2 + 4x
D) f(x) = x3 - 3x2 - 4x
Find the y-intercept of the polynomial function. 55) f(x) = -x2(x + 7)(x2 + 1)
A) 0
55)
B) 1
C) -7
D) 7
C) (- , -9]
D) (- , -4]
Find the range of the quadratic function. 56) f(x) = (x + 9)2 - 4
A) [-9, )
56)
B) [-4, )
19
Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. 57) 2x3 + 11x2 + 17x + 6 = 0 57) x
-2 -1 0 1 2 3
y1 0 -2 6 36 100 210
A) -2; The remainder is zero; -3, -2, and - 1 , or -3, -2, - 1 2
2
B) -2; The remainder is zero; 3, -2, and - 1 , or -2, - 1 , 3 2
2
C) -2; The remainder is zero; -3, -2, and 1 , or -3, -2, 1 2
2
D) -2; The remainder is zero; -3, 2, and - 1 , or -3, - 1 , 2 2
2
The graph of a quadratic function is given. Determine the function's equation.
58)
58)
A) f(x) = x2 - 4x + 4 C) j(x) = x2 + 2
B) g(x) = x2 + 4x + 4 D) h(x) = x2 - 2
Solve the problem.
59) A rectangle with width 2x + 1 inches has an area of 2x4 + 5x3 - 16x2 - 45x - 18 square inches. Write a polynomial that represents its length. A) x3 - 10x2 + 6x - 18 inches
59)
B) x3 + 2x2 - 9x - 18 inches D) x3 + 6x2 - 10x - 18 inches
C) x3 - 9x2 + 2x - 18 inches
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. 60) x3 + 6x2 + 5x - 12 = 0; -3 60)
A) {1, 4, -3}
B) {-1, 4, -3}
C) {-1, -4, -3}
Graph the polynomial function. 20
D) {1, -4, -3}
61) f(x) = 6x3 - 5x - x5
61)
A)
B)
C)
D)
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 62) f(x) = -x2(x - 2)(x + 1)
A) rises to the left and falls to the right C) rises to the left and rises to the right
62)
B) falls to the left and rises to the right D) falls to the left and falls to the right
If y varies directly as x, find the direct variation equation for the situation. 63) y = 0.6 when x = 0.3 A) y = x + 0.3 B) y = 0.3x C) y = 0.5x
21
63) D) y = 2x
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 64) f(x) = 8 - x4
A) y-axis symmetry
B) origin symmetry
Find an nth degree polynomial function with real coefficients satisfying the given conditions. 65) n = 3; - 5 and i are zeros; f(-3) = 60 A) f(x) = 3x3 + 15x2 - 3x - 15 B) f(x) = 3x3 + 15x2 + 3x + 15
C) f(x) = -3x3 - 15x2 - 3x - 15
65)
D) f(x) = -3x3 - 15x2 + 3x + 15
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 66) f(x) = (x + 3)(x + 4)(x + 5)2
A) falls to the left and falls to the right C) falls to the left and rises to the right
66)
B) rises to the left and falls to the right D) rises to the left and rises to the right
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 67) f(x) = x2 - 2
A) (1, 0)
64)
C) neither
B) (2, 0)
C) (0, -2)
Graph the rational function. 68) f(x) = -4x x+3
67)
D) (0, 2)
68)
A)
B)
22
C)
D)
Solve the problem. 69) A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. A) 5.5 inches B) 4 inches C) 5 inches D) 4.5 inches
70) An arrow is fired straight up from the ground with an initial velocity of 128 feet per second. Its
69)
70)
height, s(t), in feet at any time t is given by the function s(t) = -16t2 + 128t. Find the interval of time for which the height of the arrow is greater than 112 feet. A) before 1 sec or after 7 sec B) after 1 sec
C) between 1 and 7 sec
D) before 7 sec
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 71) f(x) = -x2 + 3x - 9 71)
A) minimum; - 27 , 3
B) minimum; 3 , - 27
C) maximum; - 27 , 3
D) maximum; 3 , - 27
4
4
2
2
2
2
4
4
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 72) f(x) = -x2 - 10x - 2
A) (5, -27)
B) (-5, 23)
C) (5, -77)
72)
D) (-10, -2)
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 73) 2x3 - 13x2 + 22x - 8 = 0 73)
A) 2, 1, 2
C) 1 , 2, 4
B) - 2, 1, -2
2
D) - 1 , 2, -4 2
Solve the problem.
74) f varies jointly as q2 and h, and f = -54 when q = 3 and h = 3. Find f when q = 2 and h = 5. A) f = -8 B) f = -20 C) f = -40 D) f = -10
23
74)
75) The amount of water used to take a shower is directly proportional to the amount of time that the
75)
shower is in use. A shower lasting 20 minutes requires 8 gallons of water. Find the amount of water used in a shower lasting 5 minutes. A) 12.5 gallons B) 1.6 gallons C) 32 gallons D) 2 gallons
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 76) f(x) = x3 + 10x2 + 33x + 36 76)
A) -3, multiplicity 2, touches the x-axis and turns around; -4, multiplicity 1, crosses the x-axis.
B) 3, multiplicity 1, crosses the x-axis;
-3, multiplicity 1, crosses the x-axis; -4, multiplicity 1, crosses the x-axis. C) 3, multiplicity 1, crosses the x-axis; -3, multiplicity 2, touches the x-axis and turns around; -4, multiplicity 1, crosses the x-axis. D) -3, multiplicity 2, crosses the x-axis; -4, multiplicity 1, touches the x-axis and turns around
Find the zeros of the polynomial function. 77) f(x) = 4(x + 1)(x + 5)4
77)
A) x = 1, x = 5, x = 4 C) x = 1, x = 4
B) x = -1, x = -5, D) x = -1, x = 4
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 78) f(x) = 3(x2 + 2)(x - 1)2 78)
A) -2, multiplicity 1, crosses the x-axis; 1, multiplicity 2, crosses the x-axis B) 1, multiplicity 2, touches the x-axis and turns around C) 1, multiplicity 2, crosses the x-axis D) -2, multiplicity 1, crosses the x-axis; 1, multiplicity 2, touches the x-axis and turns around.
24
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 79) x2 + 11x + 30 0 79)
A) [-5, )
B) (- , -6]
C) [-6, -5]
D) (- , -6] [-5, )
Find the y-intercept of the polynomial function. 80) f(x) = (x + 1)(x - 8)(x - 1)2
A) -1
80)
B) 0
C) 8
D) -8
Solve.
81) Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function increasing? A) 0 through 10 and 20 through 50
B) 0 through 10 and 25 through 40 D) 0 through 40
C) 10 through 25 and 40 through 50
25
81)
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 82) 3x + 5 0 82) 4 - 2x
A) - 5 , 2
B) - 5 ,
C) - , - 5 or (2, )
D) - 5 , 2
3
3
3
3
Solve the problem. 83) A company that produces inflatable rafts has costs given by the function C(x) = 15x + 25,000, where x is the number of inflatable rafts manufactured and C(x) is measured in dollars. The average cost to manufacture each inflatable raft is given by _ 15x + 25,000 C (x) = . x
83)
_ What is the horizontal asymptote for the function C ? Describe what this means in practical terms. A) y =25,000; 25,000 is the maximum number of inflatable rafts the company can produce.
B) y = 15; 15 is the minimum number of inflatable rafts the company can produce. C) y = 25,000; $25,000 is the least possible cost for running the company. D) y = 15; $15 is the least possible cost for producing each inflatable raft. Use the vertex and intercepts to sketch the graph of the quadratic function. 84) f(x) = 4 - (x - 2)2
26
84)
A)
B)
C)
D)
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 85) -x + 4 0 85) x-2
A) (- , 4]
B) (2, 4]
C) [2, 4]
D) (- , 2) or [4, )
27
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 86) f(x) = 7x3 - x2 + 2
A) ± 1 , ± 2 , ± 1, ± 2 7 7
B) ± 1 , ± 7 , ± 1, ± 7 2 2
C) ± 1 , ± 1 , ± 1, ± 2, ± 7
D) ± 1 , ± 2 , ± 1, ± 2, ± 7
7
2
7
7
Write an equation that expresses the relationship. Use k as the constant of variation. 87) a varies inversely as m. A) ka = m B) a = k C) a = km m
Use transformations of f(x) =
86)
87) D) a = m k
1 1 or f(x) = to graph the rational function. x x2
88) f(x) = 1 + 3
88)
x-5
A)
B)
28
C)
D)
Solve the problem. 89) A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after t seconds is s = 160t - 16t2 . For what intervals of time is the
89)
ball less than 384 above the ground (after it is tossed until it returns to the ground)? A) between 0 and 3.5 seconds and between 6.5 and 10 seconds
B) between 0 and 4.5 seconds and between 5.5 and 10 seconds C) between 0 and 4 seconds and between 6 and 10 seconds D) between 4 and 6 seconds Solve.
90) Suppose that a polynomial function is used to model the data shown in the graph below.
Determine the degree of the polynomial function of best fit and the sign of the leading coefficient. A) Degree 4; positive leading coefficient. B) Degree 4; negative leading coefficient.
C) Degree 5; negative leading coefficient.
D) Degree 5; positive leading coefficient.
29
90)
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 91) f(x) = x4 + 3x3 - 6x2 + 5x - 12
91)
A) ± 1, ± 2, ± 3, ± 4, ± 6, ± 12 B) ± 1 , ± 1 , ± 1 , ± 1 , ± 1 , ± 1, ± 2, ± 3, ± 4, ± 6, ± 12 2
3
4
6
12
C) ± 1, ± 1 , ± 1 , ± 1 , ± 1 , ± 1 2
3
4
6
12
D) ± 1 , ± 1, ± 12 12
Write an equation that expresses the relationship. Use k for the constant of proportionality. 92) x varies directly as y and inversely as the square of z. 2 A) xyz 2 = k B) x + y - z2 = k C) x = kz D) x = ky y z2
92)
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 93) x - 3 < 0 93) x+1
A) (3, )
B) (- , -1)
C) (- , -1) or (3, )
D) (-1, 3)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 94) f(x) = x4 - 2x3 + 17x2 + 18x - 234
A) {-3, 3, 1 + 6i, 1 - 6i} C) {3, -3, 1 + 5i, 1 - 5i}
B) {-3, 3, 1 + 5i, 1 - 5i} D) {3, -3, 1 + 5, 1 - 5}
30
94)
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 95) f(x) = (x - 2)2 (x2 - 9) 95)
B) -2, touches the x-axis and turns around;
A) 2, touches the x-axis and turns around;
-3, crosses the x-axis; 3, crosses the x-axis C) 2, touches the x-axis and turns around; -3, touches the x-axis and turns around; 3, touches the x-axis and turns around
9, crosses the x-axis
D) 2, touches the x-axis and turns around; 9, touches the x-axis and turns around
The graph of a quadratic function is given. Determine the function's equation.
96)
96)
A) g(x) = x2 + 2x + 1 C) j(x) = x2 + 1
B) h(x) = x2 - 1 D) f(x) = x2 - 2x + 1
Write an equation that expresses the relationship. Use k as the constant of variation. 97) d varies inversely as the square of b. 2 A) d = b B) d = k C) d = b k k b
98) s varies directly as the square of t. A) s = k t
97) D) d = k
b2
98)
B) s = k t2
C) s = k t
D) s = kt2
Find the axis of symmetry of the parabola defined by the given quadratic function. 99) f(x) = x2 + 5
A) x = 0
B) x = 5
C) y = 5
Graph the polynomial function.
31
99) D) x = -5
100) f(x) = x4 - 2x3 - x2 + 2
100)
A)
B)
C)
D)
Solve the problem. 101) h varies jointly as f and g. Find h when f = 24, g = 14, and k = 4. A) h = 84 B) h = 7 C) h = 336 3
101) D) h = 1344
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 102) f(x) = x3 - 5x
A) origin symmetry
B) y-axis symmetry 32
C) neither
102)
Solve the problem. 103) The following table shows the number of DWI arrests in a county for the years 1994-1998, where 1 represents 1994, 2 represents 1995, and so on.
103)
Year, x DWI arrests, T 1994, 1 4958.98 1995, 2 4997.8 1996, 3 5053.64 1997, 4 5082.48 1998, 5 5122.3 This data can be approximated using the third-degree polynomial T(x) = -0.67x3 + 0.53x2 + 56.92x + 4902.2. Use the Leading Coefficient Test to determine the end behavior to the right for the graph of T. Will this function be useful in modeling the number of DWI arrests over an extended period of time? Explain your answer. A) The graph of T decreases without bound to the right. Since the number of larceny thefts will eventually decrease, the function T will be useful in modeling the number of DWI arrests over an extended period of time. B) The graph of T increases without bound to the right. This means that as x increases, the values of T will become large and positive and, since the values of T will become so large, the function will no longer model the number of DWI arrests. C) The graph of T decreases without bound to the right. This means that as x increases, the values of T will become more and more negative and the function will no longer model the number of DWI arrests. D) The graph of T approaches zero for large values of x. This means that T will not be useful in modeling the number of DWI arrests over an extended period.
Determine whether the graph shown is the graph of a polynomial function.
104)
104)
A) polynomial function
B) not a polynomial function
Solve the problem.
2
105) Is there y-axis symmetry for the rational function f(x) = -8x - 8x - 12 ? 6x + 14
A) Yes
B) No
Use the vertex and intercepts to sketch the graph of the quadratic function. 33
105)
106) f(x) = x2 - 2x - 3
106)
A)
B)
C)
D)
34
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 107) 5x < x 107) x+7
A) (-7, -2) (0, )
B) (- , -7) (0, )
C) (- , 2) (7, )
D) (- , -7) (-2, 0)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 108) f(x) = 3x4 + 29x3 + 111x2 + 179x + 78
A) {-3, + 2 , -2 + 3i, -2 - 3i}
B) {-3, - 2 , -3 + 2i, -3 - 2i}
C) {3, + 2 , -2 + 3i, -2 - 3i}
D) {3, - 2 , -3 + 2i, -3 - 2i}
3
108)
3
3
3
Use the vertex and intercepts to sketch the graph of the quadratic function. 109) f(x) = 2 + 3x + x2
35
109)
A)
B)
C)
D)
Divide using long division. -15x 3 + 37x2 - 8x - 6
110)
110)
3x - 5
B) x2 + 4 +
A) -5x2 + 4x + 4 C) -5x2 + 4x + 4 + 17
4 3x - 5
D) -5x2 + 4x + 4 + 14
3x - 5
3x - 5
Find the degree of the polynomial function. 5 111) f(x) = 2 - x 6
A) 5
111)
B) - 1
C) 2
6
36
D) 0
Find the slant asymptote, if any, of the graph of the rational function. 2 112) f(x) = x - 6x + 7 x+6
A) x = y + 6 C) y = x - 12
112)
B) y = x + 13 D) no slant asymptote
Graph the polynomial function. 113) f(x) = x4 + 16x3 + 64x2
113)
A)
B)
C)
D)
37
Find the axis of symmetry of the parabola defined by the given quadratic function. 114) f(x) = (x + 2)2 + 7
A) x = 2
B) x = -2
C) y = -7
Graph the polynomial function. 115) f(x) = -x2(x + 1)(x + 3)
114) D) y = 7
115)
A)
B)
C)
D)
38
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 116) (4x - 3)(x + 5) 0 116)
A) - , 3 4
B) -5, 3 4
C) [-5, )
D) (- , -5]
3 , 4
Solve the problem. 117) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 5 x2 , but which has a minimum of 4 at x = 2.
A) f(x) = 5(x + 4)2 - 2 C) f(x) = 5(x - 2)2 + 4
117)
B) f(x) = 5(x + 2)2 + 4 D) f(x) = -5(x - 2)2 + 4
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 118) f(x) = x2 - 14 118)
A) 1 positive zero, 1 negative zero C) 1 positive zero, 0 negative zeros
B) 0 positive zeros, 0 negative zeros D) 0 positive zeros, 1 negative zero
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 119) f(x) = -2x3 + 3x2 - 4x + 8
A) ± 1 , ± 1, ± 2, ± 4 2
B) ± 1 , ± 1 , ± 1, ± 2, ± 4, ± 8 4 2
C) ± 1 , ± 1 , ± 1 , ± 1, ± 2, ± 4, ± 8
D) ± 1 , ± 1, ± 2, ± 4, ± 8
8
4
2
2
39
119)
Find the indicated intercept(s) of the graph of the function. 2 120) x-intercepts of f(x) = x + 3 x2 + 9x + 3
120)
A) ( 3, 0), (- 3, 0) C) (3, 0)
B) (3, 0) D) none
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 4 121) f(x) = x + 1 (x2 + 1)4 121) 4
A) - 1 , multiplicity 4, touches the x-axis and turns around. 4
B) - 1 , multiplicity 4, touches the x-axis and turns around; 4
-1, multiplicity 4, crosses the x-axis C) - 1 , multiplicity 4, crosses the x-axis. 4
D) 1 , multiplicity 4, touches the x-axis and turns around; 4
1, multiplicity 4, crosses the x-axis
Find the indicated intercept(s) of the graph of the function. 2 122) y-intercept of f(x) = x - 7x + 7 10x
A) (0, 7)
122)
B) 0, - 10
C) 0, 7
7
10
D) none
Solve.
123) When the temperature stays the same, the volume of a gas is inversely proportional to the
pressure of the gas. If a balloon is filled with 54 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 9 cubic inches. A) 78 pounds per square inch B) 9 pounds per square inch 14
C) 84 pounds per square inch
D) 70 pounds per square inch
40
123)
Solve the problem. 124) The following table shows the number of larceny thefts in a county for the years 1994-1998, where 1 represents 1994, 2 represents 1995, and so on.
124)
Year, x Larceny Thefts, T 1994, 1 4652.48 1995, 2 4698.24 1996, 3 4741.94 1997, 4 4775.04 1998, 5 4823 This data can be approximated using the third-degree polynomial T(x) = -0.59x3 + 0.51x2 + 55.36x + 4597.2.
Use this function to predict the number of larceny thefts in 2007. Round to the nearest whole number. A) 3853 B) 3078 C) 3846 D) -734
125) y varies jointly as a and b and inversely as the square root of c. y = 10 when a = 2, b = 10, and c = 36. Find y when a = 6, b = 3, and c = 4. A) 108 B) 13.5
C) 9
125)
D) 27
126) Two people are 31 years old and 25 years old, respectively. In x years from now, their ages can be
126)
represented by x + 31 and x + 25. Use long division to find the ratio of the older person's age to the younger person's age in x years. A) 1.2400 B) 1 + 56 C) 1 + 56 D) 1 + 6 x + 25 x + 31 x + 25
Use transformations of f(x) =
1 1 or f(x) = to graph the rational function. x x2
127) f(x) = 1
127)
x-5
41
A)
B)
C)
D)
Use synthetic division and the Remainder Theorem to find the indicated function value. 128) f(x) = x4 + 8x3 - 2x2 + 4x - 5; f - 1 4
A) - 25 4
B) - 1599
C) 1599
256
256
Divide using synthetic division. 129) (x5 - 4x4 - 6x3 + x2 - x + 46) ÷ (x + 2)
128) D) 1599 1024
129)
A) x4 - 6x3 + 6x2 - 11x - 21 + 4
B) x4 - 6x3 + 6x2 - 12x + 21 + 10
C) x4 - 6x3 + 6x2 - 12x - 22 + 10
D) x4 - 6x3 + 6x2 - 11x + 21 + 4
x+2
x+2
x+2
x+2
42
Solve.
130) While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the
130)
car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 8 feet per second per second when the radius of the turn is 80 feet, find the acceleration the passengers feel when the radius of the turn is 160 feet. A) 6 feet per second per second B) 4 feet per second per second
C) 7 feet per second per second
D) 5 feet per second per second
Solve the problem.
131) Solve the equation 3x3 - 31x2 + 82x - 24 = 0 given that 4 is a zero of f(x) = 3x3 - 31x2 + 82x - 24. A)
1 4, 6, 3
B) 4, 1, 2
C)
1 4, -6, 3
131)
D) 4, -1, - 2
132) The power that a resistor must dissipate is jointly proportional to the square of the current flowing
132)
through the resistor and the resistance of the resistor. If a resistor needs to dissipate 108 watts of power when 6 amperes of current is flowing through the resistor whose resistance is 3 ohms, find the power that a resistor needs to dissipate when 3 amperes of current are flowing through a resistor whose resistance is 9 ohms. A) 162 watts B) 243 watts C) 81 watts D) 27 watts
Find the axis of symmetry of the parabola defined by the given quadratic function. 133) f(x) = -x2 - 6x + 1
A) x = -6
B) x = 10
C) x = -3
133) D) x = 3
Solve the problem. 134) April shoots an arrow upward into the air at a speed of 32 feet per second from a platform that is 12 feet high. The height of the arrow is given by the function h(t) = -16t2 + 32t + 12, where t is the time is seconds. What is the maximum height of the arrow? A) 12 ft B) 16 ft C) 11 ft
Graph the rational function. 2 135) f(x) = x - 3x (x - 2)2
134)
D) 28 ft
135)
43
A)
B)
C)
D)
Divide using long division. 136) (15x3 - 3) ÷ (5x - 1)
A) 3x2 + 3 x + 3 5
25
136) 72 25(5x - 1)
B) 3x2 - 3 x + 3 5
C) 3x2 + 3 x + 3 5
25
D) 3x2 + 3 x + 3 +
25
5
25
72 25(5x - 1)
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 137) f(x) = 7x5 - 4x2 + 5x - 1
A) ± 1, ± 1 7
B) ± 7, ± 1
C) ± 1, ± 7
7
137) D) ± 1, ± 7, ± 1 7
Solve the problem. 138) A company that produces radios has costs given by the function C(x) = 20x + 15,000 , where x is the number of radios manufactured and C(x) is measured in dollars. The average cost to manufacture each radio is given by _ 20x + 15,000 C (x) = . x _ Find C (50). (Round to the nearest dollar, if necessary.) A) $51 B) $50 C) $320
44
D) $310
138)
Find the y-intercept of the polynomial function. 139) f(x) = -x2 - 2x + 8
A) -1
139) C) 8
B) -8
D) 0
Determine whether the function is a polynomial function. 140) f(x) = 3x3 + 4x2 - 3x-5 + 100
140)
A) Yes
B) No
Solve the problem. 141) If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 6 volts are applied to a circuit, 150 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 8 volts. A) 48 milliamperes B) 192 milliamperes
C) 200 milliamperes
D) 225 milliamperes 2
142) Is there origin symmetry for the rational function f(x) = 9x - 2 ?
142)
-8x2 + 1
A) Yes
B) No
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 143) f(x) = -2x2 + 4x + 7
A) (2, 3)
141)
B) (-2, -9)
C) (-1, 1)
Solve the problem.
144) Is there y-axis symmetry for the rational function f(x) = A) Yes
-6x2 ? -2x3 - 19
B) No
45
143)
D) (1, 9)
144)
Solve.
145) Suppose that a polynomial function is used to model the data shown in the graph below.
145)
Determine the degree of the polynomial function of best fit and the sign of the leading coefficient. A) Degree 4; positive leading coefficient. B) Degree 4; negative leading coefficient.
C) Degree 3; negative leading coefficient.
D) Degree 3; positive leading coefficient.
Solve the problem.
146) Solve the equation 8x3 - 34x2 + 5x + 12 = 0 given that - 1 is a root.
146)
2
A) - 1 , - 1, -3 2
B) - 1 , - 3 , -4 2
C) - 1 , 1, 3
4
2
D) - 1 , 3 , 4 2 4
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 147) x3 + 6x2 - 14x + 16 = 0 147)
A) {1 + i, 1 - i, -8}
B) {1 + i, 1 - i, 8i}
C) {1 + i, 1 - i, 8}
D) {-8, 8}
Use synthetic division and the Remainder Theorem to find the indicated function value. 148) f(x) = 6x4 + 2x3 + 3x2 - 4x + 40; f(3)
A) 813
B) 1567
C) 595
Graph the polynomial function. 149) f(x) = 3x(x + 2)3
148) D) 377
149)
46
A)
B)
C)
D)
47
150) f(x) = (x + 1)(x + 3)(x + 5)
150)
A)
B)
C)
D)
151) f(x) = x4 - 4x3 + 4x2
151)
48
A)
B)
C)
D)
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 152) f(x) = (x + 3)2 - 5
A) (3, 5)
B) (-3, -5)
C) (3, -5)
152)
D) (-3, 5)
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. 153) 6x3 + 11x2 - 92x + 15 = 0; 3 153)
A) 1 , 5, 3 6
B) - 1 , -5, 3
C) 1 , -5, 3
6
6
Write an equation that expresses the relationship. Use k as the constant of variation. 154) w varies jointly as x and the cube of y. A) wxy3 = k B) w = kxy3 C) w = k + x + y3
49
D) - 5 , 1, 3 6
154) D) w + x + y3 = k
Determine whether the graph shown is the graph of a polynomial function.
155)
155)
A) polynomial function
B) not a polynomial function
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. 156) Crosses the x-axis at -1, 0, and 3; lies above the x-axis between -1 and 0; lies below the x-axis 156) between 0 and 3. A) f(x) = x3 + 2x2 - 3x B) f(x) = x3 - 2x2 - 3x
C) f(x) = - x3 - 2x2 + 3x
D) f(x) = -x3 + 2x2 + 3x
Solve the problem. 157) Among all pairs of numbers whose difference is 50, find a pair whose product is as small as possible. A) -75 and -25 B) 25 and 25 C) 75 and 25 D) -25 and 25 Find the y-intercept for the graph of the quadratic function. 158) f(x) = 3x2 - 4x - 7
A) 0, 7 3
158)
B) (0, -7)
C) (0, 7)
D) 0, - 7 3
C) 5
D) 7
Find the degree of the polynomial function. 159) f(x) = -4x + 7x5
A) -4
159)
B) 1
Find the domain and range of the quadratic function whose graph is described. 160) The minimum is 4 at x = 1. A) Domain: (- , ) B) Domain: (- , ) Range: (- , 4] Range: [1, ) C) Domain: [1, ) D) Domain: (- , ) Range: [4, ) Range: [4, )
160)
Find the y-intercept for the graph of the quadratic function. 161) y + 4 = (x - 2)2
A) (0, 4)
157)
161)
B) (4, 0)
C) (0, 0) 50
D) (0, -4)
The graph of a quadratic function is given. Determine the function's equation.
162)
162)
A) f(x) = (x + 1)2 + 1 C) j(x) = (x - 1)2 - 1
B) h(x) = (x - 1)2 + 1 D) g(x) = (x + 1)2 - 1
51
Graph the polynomial function.
163) f(x) = (x + 1)(x + 3)(x + 5)2
163)
A)
B)
C)
D)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 164) f(x) = 2x4 - 19x3 + 71x2 - 109x + 39
A) {-3, 1 , 3 + 2i, 3 - 2i} 2
B) {3, - 1 , 2 + 3i, 2 - 3i} 2
C) {3, 1 , 3 + 2i, 3 -2i}
D) {-3, - 1 , 2 + 3i, 2 - 3i}
2
Use transformations of f(x) =
2
1 1 or f(x) = to graph the rational function. x x2
52
164)
165) f(x) =
1
(x - 4)2
+3
165)
A)
B)
C)
D)
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 166) f(x) = x2 (x - 1)(x - 3) 166)
A) 0, crosses the x-axis;
B) 0, touches the x-axis and turns around;
1, crosses the x-axis; 3, crosses the x-axis C) 0, crosses the x-axis; 1, touches the x-axis and turns around; 3, touches the x-axis and turns around
-1, crosses the x-axis; -3, crosses the x-axis D) 0, touches the x-axis and turns around; 1, crosses the x-axis; 3, crosses the x-axis
53
Find the x-intercepts (if any) for the graph of the quadratic function. 167) f(x) = -x2 + 9x - 20
A) No x-intercepts C) (4, 0) and (-5, 0)
167)
B) (4, 0) and (5, 0) D) (-4, 0) and (-5, 0)
168) f(x) = x2 + 12x + 15 Give your answers in exact form. A) (6 ± 15, 0) B) (-12 ± 15, 0) C) (6 + 21, 0)
168) D) (-6 ± 21, 0)
Find the indicated intercept(s) of the graph of the function. 2 169) y-intercept of f(x) = x - 15 x2 + 8x - 14
A) 0, 15
169)
B) 0, - 14
14
C) (0, 15)
15
D) none
Solve the problem. 170) If y varies directly as the square of x, and y = 90 when x = 2, find y when x = 6. A) 30 B) 10 C) 810 D) 270
170)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 171) 3x2 - 4x 7 171)
A) -1, 7 3
B) (- , -1] 7 , 3
C) -1, 7 3
D) (- , -1)
7 , 3
54
Solve the problem. 172) The perimeter of a rectangle is 54 feet. Describe the possible lengths of a side if the area of the rectangle is to be greater than 152 square feet. A) The length of the rectangle must lie between 8 and 19 ft
172)
B) The length of the rectangle must be greater than 19 ft or less than 8 ft C) The length of the rectangle must lie between 1 and 152 ft D) The length of the rectangle must be greater than 19 ft 173) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 11x2 , but which has its vertex at (5, 6).
A) f(x) = 11(x + 5)2 + 6 C) f(x) = (11x + 5)2 + 6
173)
B) f(x) = 11(x + 6)2 + 5 D) f(x) = 11(x - 5)2 + 6
174) An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet of
174)
the arrow t seconds after it was shot into the air is given by the function h(x) = -16t2 + 160t. Find the maximum height of the arrow. A) 720 ft B) 400 ft C) 1200 ft D) 80 ft
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 175) f(x) = -x3(x + 4)2 (x - 6)
A) origin symmetry
B) y-axis symmetry
C) neither
Solve the problem. 176) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 232 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 6728 ft2 B) 3364 ft2 C) 10,092 ft2 D) 13,456 ft2 Determine the constant of variation for the stated condition. 177) z varies directly as x and inversely as y, and z = 4 when x = 52 and y = 52. A) k = 1 B) k = 1 C) k = 4 4
B) 8
C) 0
176)
177) D) k = 13
Determine the maximum possible number of turning points for the graph of the function. 178) f(x) = 5x8 - 8x7 - 9x - 25
A) 7
175)
178)
D) 5
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 179) x3 + 2x2 - 9x - 18 = 0 179)
A) {-3, 2, 3}
B) {-3, -2, 3}
C) {-2}
55
D) {-3}
Find an nth degree polynomial function with real coefficients satisfying the given conditions. 180) n = 4; 2i, 3, and -3 are zeros; leading coefficient is 1 A) f(x) = x4 + 4x2 - 36 B) f(x) = x4 - 5x2 - 36
180)
D) f(x) = x4 + 4x3 - 5x2 - 36
C) f(x) = x4 + 4x2 - 3x - 36
Use the vertex and intercepts to sketch the graph of the quadratic function. 181) f(x) = 8 - x2 - 2x
A)
B)
C)
D)
56
181)
Divide using long division. 5r3 - 23r2 - 5r - 25
182)
182)
r- 5
A) 5r2 + 2r + 5
B) 5r2 + 2r + 5
C) 5r2 - 2r - 5
r- 5
D) r2 + 5r + 2
Write an equation that expresses the relationship. Use k as the constant of variation. 183) a varies jointly as y and the difference between p and z.
A) a = k(yp - z)
B) a = ky + p - z
C) a = ky(p - z)
183) D) a = ky (p - z)
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 184) f(x) = x(2 - x2)
A) origin symmetry
B) y-axis symmetry
Find the variation equation for the variation statement. 185) z varies jointly as y and the cube of x; z = 384 when x = 4 and y = -3 A) y = 2x3 y B) y = -2x3 y C) y = -2xy3 Graph the rational function. 186) f(x) = x - 2 x2 - x - 56
184)
C) neither
185) D) y = 2xy3
186)
57
A)
B)
C)
D)
Find the y-intercept for the graph of the quadratic function. 187) f(x) = x2 + 7x - 10
A) (0, 7)
187)
B) (0, 10)
C) (0, 2)
D) (0, -10)
Determine whether the function is a polynomial function. 3 188) f(x) = 16x3 + 7x + x
188)
A) No
B) Yes
Divide using long division. x4 - 2x3 - 10x2 + 5x + 36
189)
189)
x2 - 3x - 4
B) x2 + x - 3 +
A) x2 - 6x + 4 C) x2 - 6x + 4 + 8x - 28
D) x2 + x - 3
x2 - 3x - 4
Graph the rational function. 58
24 2 x - 3x - 4
2
190) f(x) = x + 3x - 4
190)
x2 - 1
A)
B)
C)
D)
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 191) f(x) = x + 2x2 - 5x3
A) falls to the left and rises to the right C) rises to the left and rises to the right
B) rises to the left and falls to the right D) falls to the left and falls to the right
59
191)
Solve the problem.
192) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -5p2 + 1720p,
192)
193) f varies jointly as q2 and h, and f = 54 when q = 3 and h = 2. Find q when f = 288 and h = 6. A) q = 6 B) q = 4 C) q = 2 D) q = 3
193)
when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? A) $295,840 B) $591,680 C) $1,183,360 D) $147,920
Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. 194) x3 + 6x2 + 11x + 6 = 0 194)
A) -1; The remainder is zero; -1, -2, and -3, or {-3, -2, -1} B) -1; The remainder is zero; -1, -2, and 3, or {-2, -1, 3} C) -1; The remainder is zero; -1, 2, and -3, or {-3, -1, 2} D) -1; The remainder is zero; 1, -2, and -3, or {-3, -2, 1} Determine the maximum possible number of turning points for the graph of the function. 195) f(x) = (2x + 3)2( x2 - 1)(x + 1)
A) 10
B) 2
C) 5
D) 4
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 196) f(x) = -5(x2 + 1)(x + 1)2
A) rises to the left and falls to the right C) falls to the left and falls to the right
195)
196)
B) rises to the left and rises to the right D) falls to the left and rises to the right
Find the vertical asymptotes, if any, of the graph of the rational function. 197) f(x) = x x2 + 7
A) x = 7 C) x = -7
B) x = -7, x = 7 D) no vertical asymptote
60
197)
Find the range of the quadratic function. 198) f(x) = 4 - (x + 3)2
A) (- , 4]
198)
B) (- , 3]
C) [-3, )
D) [4, )
Solve.
199) If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to
199)
the resistance, R. If the current is 420 milliamperes when the resistance is 2 ohms, find the current when the resistance is 14 ohms. A) 2940 milliamperes B) 2933 milliamperes
C) 120 milliamperes
D) 60 milliamperes
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 200) f(x) = (x + 1)(x + 3)(x + 5)3
A) rises to the left and falls to the right C) rises to the left and rises to the right
B) falls to the left and rises to the right D) falls to the left and falls to the right
Determine the constant of variation for the stated condition. 201) g varies directly as f2 , and g = 45 when f = 3.
A) k = 45
200)
B) k = 1
201) C) k = 42
5
D) k = 5
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 202) f(x) = 5x7 - 3x2 + x + 7 202)
A) 3 or 1 positive zeros, 3 or 1 negative zeros B) 2 or 0 positive zeros, 2 or 0 negative zeros C) 2 or 0 positive zeros, 1 negative zero D) 2 or 0 positive zeros, 1 or 0 negative zeros Find the coordinates of the vertex for the parabola defined by the given quadratic function. 203) f(x) = (x + 5)2 + 4
A) (-5, 4)
B) (4, -25)
C) (4, -5)
203)
D) (-4, 5)
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 204) f(x) = 10x3 + 10x2 + 4x + 5; between -2 and -1 204)
A) f(-2) = 43 and f(-1) = -1; yes C) f(-2) = -43 and f(-1) = -1; no
B) f(-2) = -43 and f(-1) = 1; yes D) f(-2) = 43 and f(-1) = 1; no
61
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 205) f(x) = (x + 1)(x - 6)(x - 1)2 205)
A) 1, crosses the x-axis;
B) -1, crosses the x-axis;
-6, touches the x-axis and turns around; -1, touches the x-axis and turns around C) -1, crosses the x-axis; 6, crosses the x-axis; 1, crosses the x-axis
6, crosses the x-axis; 1, touches the x-axis and turns around D) 1, crosses the x-axis; -6, crosses the x-axis; -1, touches the x-axis and turns around
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. 206) Touches the x-axis at 0 and crosses the x-axis at 4; lies above the x-axis between 0 and 4. 206) A) f(x) = -x3 - 4x2 B) f(x) = -x3 + 4x2
C) f(x) = x3 - 4x2
D) f(x) = x3 + 4x2
Graph the polynomial function. 207) f(x) = 1 - 1 x4 2 2
207)
A)
B)
62
C)
D)
Graph the rational function. 2 208) f(x) = 3x x2 + 4
208)
A)
B)
63
C)
D)
Use transformations of f(x) =
1 1 or f(x) = to graph the rational function. x x2
209) f(x) = 1 - 2
209)
x2
A)
B)
64
C)
D)
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 210) 3x4 + 23x3 + 71x2 + 77x + 26 = 0 210)
A) {-1, + 2 , -2 + 3i, -2 - 3i}
B) {1, - 2 , -3 + 2i, -3 - 2i}
C) {1, + 2 , -2 + 3i, -2 - 3i}
D) {-1, - 2 , -3 + 2i, -3 - 2i}
3
3
3
3
Find the domain of the rational function. 211) h(x) = x + 9 x2 - 25
211)
A) {x|x -5, x 5, x -9} C) {x|x -5, x 5}
B) all real numbers D) {x|x 0, x 25}
Find the indicated intercept(s) of the graph of the function. 2 212) y-intercept of f(x) = x - 2x x2 + 6x - 7
A) 0, 2 7
212)
B) 0, - 7
C) (0, 0)
2
Find the vertical asymptotes, if any, of the graph of the rational function. 213) h(x) = x x(x + 1)
A) x = 0 and x = -1 C) x = 0 and x = 1
D) (0, 2)
213)
B) x = -1 D) no vertical asymptote
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 214) x4 - 3x3 + 2x2 + 16x - 16 = 0 214)
A) {-2, 1, 2 + 2i, 2 - 2i} C) {2, -1, 2 + 2, 2 - 2}
B) {2, -1, 2 + 2i, 2 - 2i} D) {-2, 1, 2 + 3i, 2 - 3i}
Graph the rational function.
65
2
215) f(x) = x - 2x + 1
215)
(x - 5)2
A)
B)
C)
D)
66
2
216) f(x) = x - x - 56
216)
x2 - 1
A)
B)
C)
D)
Find the axis of symmetry of the parabola defined by the given quadratic function. 217) f(x) = 7x2 - 14x + 5
A) x = 2
B) x = 1
C) x = -1 67
217) D) x = -2
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
218)
218)
A) origin symmetry
B) y-axis symmetry
C) neither
Find the zeros of the polynomial function. 219) f(x) = x3 + x2 - 12x
219)
A) x = - 4, x = 3 C) x = 0, x = - 4, x = 3
B) x = 2, x = 3 D) x = 0, x = 2, x = 3
Divide using long division. 220) (5x4 - 32x3 - 20x2 - 13x + 42) ÷ (7 - x)
220)
A) -5x3 - 3x2 - x - 6 + 84 7-x
B) -5x3 - 3x2 - x + 6
C) -5x3 - 3x2 - x - 6
D) -5x3 - 3x2 + x - 6
Determine whether the function is a polynomial function. 221) f(x) = 4x + 2x2
221)
A) Yes
B) No
Find the slant asymptote, if any, of the graph of the rational function. 3 222) f(x) = x + 5 x2 + 9x
A) y = x + 5 Use transformations of f(x) =
B) y = x - 9
C) y = x
1 1 or f(x) = to graph the rational function. x x2
68
222) D) y = x + 9
223) f(x) = 1 - 4
223)
x
A)
B)
C)
D)
Graph the polynomial function.
69
224) f(x) = 3x2 - x3
224)
A)
B)
C)
D)
Find the degree of the polynomial function. 225) -10x3 - 8x2 + 6x - 5y4 + 5
A) 4
225) C) 10
B) -10
D) 3
Solve the problem.
226) Use synthetic division to divide f(x) = x3 - 1x2 - 52x + 160 by x + 8. Use the result to find all zeros of f.
A) {8, 4, 5}
B) {-8, 4, 5}
C) {-8 , -4, -5}
70
D) {8, -4, -5}
226)
227) y varies jointly as x and z. y = 2.7 when x = 45 and z = 6. Find y when x = 30 and z = 6. A) 1.8 B) 18 C) 180 D) 3.6 Write an equation that expresses the relationship. Use k as the constant of variation. 228) d varies jointly as b and the sum of p and c. A) d = kb + p + c B) d = kb(p + c) C) d = kb (p + c)
227)
228) D) d = k(bp + c)
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 229) f(x) = 6x5 - 7x3 + 6x2 - 2; between -2 and -1 229)
A) f(-2) = -114 and f(-1) = -5; no C) f(-2) = -114 and f(-1) = 5; yes
B) f(-2) = 114 and f(-1) = -5; yes D) f(-2) = 114 and f(-1) = 5; no
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 230) f(x) = x3 + 6x2 + 21x + 26
B) {-2, 3 + 5, 3 - 5} D) {-2, -2 + 3i, -2 - 3i}
A) {-2, 3 + 2i, 3 - 2i} C) {2, -2 + 5, -4 - 5}
Use synthetic division and the Remainder Theorem to find the indicated function value. 231) f(x) = x4 - 9x3 - 8x2 - 9x - 2; f(-3)
A) -277
230)
C) 277
B) -831
231) D) 196
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 232) f(x) = x3 + 9x2 + 24x + 20 232)
A) 2, crosses the x-axis;
-2, crosses the x-axis; -5, crosses the x-axis. B) 2, crosses the x-axis; -2, touches the x-axis and turns around; -5, crosses the x-axis. C) -2, crosses the x-axis; -5, touches the x-axis and turns around D) -2, touches the x-axis and turns around; -5, crosses the x-axis.
Find the degree of the polynomial function. 233) f(x) = 5x - x4 + 5 4
A) -1
233)
B) 5
C) 4
71
D) 1
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 234) x2 - 8x + 12 > 0 234)
A) (2, 6)
B) (- , 2)
C) (- , 2) (6, )
D) (6, )
Write an equation that expresses the relationship. Use k as the constant of variation. 235) The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 5? A) The weight is multiplied by 5 B) The weight is divided by 25
C) The weight is divided by 5
235)
D) The weight is multiplied by 25
Solve the problem. 236) You drive 98 miles along a scenic highway and then take a 22-mile bike ride. Your driving rate is 3 times your cycling rate. Suppose you have no more than a total of 7 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Write a rational inequality that can be used to determine the possible values of x. Do not simplify and do not solve the inequality. A) 3x + x 7 B) 98 + 22 7 C) 98 + 22 7 D) 98 + 22 7 98 22 3x x 3x x x 3x
236)
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 237) f(x) = x5 - 2.1x4 - 14.44x3 + 3x2 + 41.67x - 15.216 237)
A) 3 or 1 positive zeros, 3 or 1 negative zeros B) 3 or 1 positive zeros, 2 or 0 negative zeros C) 2 or 0 positive zeros, 2 or 0 negative zeros D) 2 or 0 positive zeros, 3 or 1 negative zeros
72
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 238) x2 + 9x 0 238)
A) (- , -9] [0, ]
B) [-9, 0]
C) [0, ]
D) (- , -9]
Find the domain of the rational function. 9x 239) f(x) = (x + 5)(x + 3)
239)
A) {x|x 5, x 3} C) {x|x -5, x -3}
B) all real numbers D) {x|x -5, x -3, x -9}
Find the x-intercepts (if any) for the graph of the quadratic function. 240) 5x2 + 8x + 2 = 0 Give your answers in exact form. A) -4 ± 6 , 0 B) -4 ± 26 , 0 5 5
240)
C) -8 ± 6 , 0 5
If y varies inversely as x, find the inverse variation equation for the situation. 241) y = 20 when x = 8 A) y = x B) y = 1 C) y = 160 160 160x x
D) -4 ± 6 , 0 10
241) D) y = 5 x 2
Divide using long division. -4t4 + 18t3 + 8t2 - 60t - 40
242)
242)
2t2 - 4t - 4
A) -2t2 - 5t + 10
B) -2t2 + 6t + 10
C) -2t2 + 5t + 10
Find the slant asymptote, if any, of the graph of the rational function. 2 243) f(x) = 8x 2 4x + 6
A) y = x + 2 C) y = 8x
B) y = x + 8 D) no slant asymptote
73
D) -2t2 + 5t - 10
243)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 244) x2 + 6x + 9 > 0 244)
A) (- , -3) (-3, )
B) (-3, )
C) (- , )
D) (- , -3)
Solve the problem.
2 245) Is there y-axis symmetry for the rational function f(x) = 8x
5x4 - 5
A) Yes
?
245)
B) No
Find the y-intercept for the graph of the quadratic function. 246) f(x) = (x + 1)2 - 1
A) (0, 2)
246)
B) (0, -1)
C) (0, 1)
Find the indicated intercept(s) of the graph of the function. 2 247) x-intercepts of f(x) = x + 3x x2 + 3x - 9
D) (0, 0)
247)
A) (-3, 0) C) (3, 0)
B) (0, 0) and (-3, 0) D) (0, 0) and (3, 0)
74
Solve the problem. 248) The polynomial function H(x) = - 0.001183 x4 + 0.05495 x3 - 0.8523x2 + 9.054 x + 6.748
248)
models the age in human years, H(x), of a dog that is x years old, where x 1. Using the graph of this function shown below, what is the approximately equivalent dog age for a person who is 60?
A) 11 years
B) 8.5 years
C) 12.5 years
D) 9 years
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 249) f(x) = x4 - 100x2 249)
A) 0, crosses the x-axis;
10, crosses the x-axis; -10, crosses the x-axis B) 0, touches the x-axis and turns around; 100, touches the x-axis and turns around C) 0, touches the x-axis and turns around; 10, crosses the x-axis; -10, crosses the x-axis D) 0, touches the x-axis and turns around; 100, crosses the x-axis
Write an equation that expresses the relationship. Use k for the constant of proportionality. 250) s varies directly as the square of t and inversely as the cube of u. 2 3 A) s + t2 - u3 = k B) st2 u3 = k C) s = kt D) s = ku u3 t2
75
250)
Solve the problem. 251) A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 20 inches by 14 inches, what size square must be cut if the volume of the box is to be 288 cubic inches?
A) 4 in. by 4 in. square C) 6 in. by 6 in. square
B) 12 in. by 12 in. square D) 3 in. by 3 in. square
Find the axis of symmetry of the parabola defined by the given quadratic function. 252) f(x) = 11(x - 3)2 + 9
A) x = 9
251)
B) x = -3
C) x = 3
If y varies inversely as x, find the inverse variation equation for the situation. 253) y = 9 when x = 2 A) y = 1 B) y = 9 x C) y = 18 18x 2 x Use the vertex and intercepts to sketch the graph of the quadratic function. 254) f(x) = -x2 - 4x - 3
76
252) D) x = 11
253) D) y = x 18
254)
A)
B)
C)
D)
Solve the problem.
255) y varies directly as z2 and y = 125 when z = 5. Find y when z = 3. A) 75 B) 25 C) 15
255) D) 45
256) You have 72 feet of fencing to enclose a rectangular plot that borders on a river. If you do not
256)
fence the side along the river, find the length and width of the plot that will maximize the area. A) length: 36 feet, width: 36 feet B) length: 18 feet, width: 18 feet
C) length: 36 feet, width: 18 feet
D) length: 54 feet, width: 18 feet
257) The daily profit in dollars of a specialty cake shop is described by the function
257)
P(x) = -5x2 + 210x - 1600, where x is the number of cakes prepared in one day. The maximum
profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit? A) 21 cakes B) 42 cakes C) 441 cakes D) 2205 cakes
Find the vertical asymptotes, if any, of the graph of the rational function. x-9 258) 2 x - 10x + 24
A) x = 6, x = 4, x = - 9 C) x = 6, x = 4
B) x = -6, x = -4 D) x = - 9
77
258)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 259) (x + 6)(x + 4)(x + 2) < 0 259)
A) (-2, )
B) (-6, -4) (-2, )
C) (- , -4)
D) (- , -6) (-4, -2)
Write an equation that expresses the relationship. Use k as the constant of variation. 260) a varies jointly as g and the square of z.
A) a = kg z2
B) a =kgkz 2
C) a = kgz 2
260) D) a = kz
2
g
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 261) f(x) = 3x3 - 3x3 - x5
A) falls to the left and falls to the right C) falls to the left and rises to the right
B) rises to the left and rises to the right D) rises to the left and falls to the right
78
261)
Use the graph of the rational function shown to complete the statement.
262)
262)
As x -2 - , f(x) ? A) +
B) 0
C) 2
D) -
Divide using synthetic division. 263) (x4 + 16) ÷ (x - 2)
A)
263)
16 x3 + 2x 2 + 4x + 8 + x-2
B) x3 + 2x2 + 4x + 8
C) x3 - 2x2 + 4x - 8 + 32
D) x3 + 2x2 + 4x + 8 + 32
x-2
x-2
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 264) -x - 2 0 264) x+3
A) (-3, -2]
B) (- , -3] or [-2, )
C) [-2, )
D) (- , -3) or [-2, )
If y varies directly as x, find the direct variation equation for the situation. 265) y = 0.5 when x = 4 A) y = x - 3.5 B) y = 0.125x C) y = 0.5x
265) D) y = 8x
Solve the problem. 266) The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004x2 + 3.2x - 400. Find the number of pretzels that must be sold to maximize profit.
A) 240 pretzels
B) 800 pretzels
C) 400 pretzels
79
D) 1.6 pretzels
266)
267) The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the
267)
room and the height of the wall. If a room with a perimeter of 75 feet and 8-foot walls requires 6 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 45 feet and 6-foot walls. A) 27 quarts B) 2.7 quarts C) 5.4 quarts D) 270 quarts
Divide using long division. 4m 3 + 21m 2 - 42m + 49
268)
268)
m+7
A) m 2 + 8m + 9
B) 4m 2 + 7m + 7
C) m 2 + 7m + 4
D) 4m 2 - 7m + 7
The graph of a quadratic function is given. Determine the function's equation.
269)
269)
A) h(x) = -x2 - 3 C) g(x) = -x2 + 6x + 9
B) f(x) = -x2 - 6x - 9 D) j(x) = -x2 + 3
Find the horizontal asymptote, if any, of the graph of the rational function. 2 270) g(x) = 12x 3x2 + 1
270)
A) y = 1
B) y = 0
C) y = 4
D) no horizontal asymptote
4
Solve the problem.
271) x varies inversely as y2 , and x = 6 when y = 8. Find x when y = 2. A) x = 96 B) x = 24 C) x = 144
80
271) D) x = 4
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 272) (6z + 1)(3z - 8) > 0 272)
A) - 1 , 8 6 3
B) - , - 1 6
8 , 3
C) 8 , 3
D) - 1 , 8 6 3
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 273) 3x3 - x2 - 21x + 7 = 0 273)
A) {- 1 , 7, - 7}
B) { 1 , 7, - 7}
C) {3, 7, - 7}
D) {-3, 7, - 7}
3
3
The graph of a quadratic function is given. Determine the function's equation.
274)
274)
A) f(x) = x2 - 2x + 1 C) h(x) = x2 - 1
B) j(x) = x2 + 1 D) g(x) = x2 + 2x + 1
81
Find the y-intercept of the polynomial function. 275) f(x) = -x2(x + 4)(x2 - 1)
A) -4
275) C) 4
B) -1
D) 0
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 276) 9x3 + 27x2 - 16x - 48 > 0 276)
A) (- , -3]
-
4 4 , 3 3
B) (- , -3)
-
4 4 , 3 3
C) 4 , 3
D) -3, - 4 3
4 , 3
Solve the problem.
2
277) Is there origin symmetry for the rational function f(x) = 4x + 2 ? -9x
A) Yes
B) No
Use the vertex and intercepts to sketch the graph of the quadratic function.
82
277)
278) f(x) = - 4x + 3 + x2
278)
A)
B)
C)
D)
83
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 279) 3x2 + 14x - 24 0 279)
A) [-6, )
B) -6, 4
C) - , 4
D) (- , -6]
3
3
4 , 3
Write an equation that expresses the relationship. Use k as the constant of variation. 280) g varies directly as v. A) k = gv B) g = kv C) g = k v
280) D) v = k g
Find the y-intercept of the polynomial function. 281) f(x) = x2 (x - 1)(x - 6)
A) -1
281)
B) 6
C) -6
D) 0
Solve.
282) If the force acting on an object stays the same, then the acceleration of the object is inversely
282)
proportional to its mass. If an object with a mass of 28 kilograms accelerates at a rate of 6 meters per second per second by a force, find the rate of acceleration of an object with a mass of 4 kilograms that is pulled by the same force. A) 36 meters per second per second B) 6 meters per second per second 7
C) 42 meters per second per second
D) 35 meters per second per second
Determine the constant of variation for the stated condition. 283) t varies jointly as r and s, and t = 1872 when r = 36 and s = 13. A) k = 1 B) k = 9 C) k = 1 4 9
84
283) D) k = 4
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 284) x > 0 284) x+2
A) (0, )
B) (- , -2) or (0, )
C) (-2, 0]
D) (- , -2] or [0, )
Write an equation that expresses the relationship. Use k for the constant of proportionality. 285) w varies directly as the square of x and inversely as y. 2 A) w = k + x2 - y2 B) w = kx y
D) w = ky
C) w = kx2 y
Divide using synthetic division. 286) (x2 + 14x + 45) ÷ (x + 5)
A) x - 40
285)
x2
286) B) x3 - 40
C) x2 + 9
Find the domain and range of the quadratic function whose graph is described. 287) The vertex is (1, -13) and the graph opens up. A) Domain: (- , ) B) Domain: (- , ) Range: (- , -13] Range: [-13, ) C) Domain: [1, ) D) Domain: (- , ) Range: [-13, ) Range: [1, )
D) x + 9
287)
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 288) f(x) = -5x2 + 10x 288)
A) minimum; - 1, - 5 C) maximum; - 1, - 5
B) maximum; 1, 5 D) minimum; 1, 5
Find the slant asymptote, if any, of the graph of the rational function. 2 289) f(x) = x + 16 x
A) y = x + 16 C) x = 0
B) y = x D) no slant asymptote
85
289)
Solve the problem. 290) The average cost per unit, y, of producing x units of a product is modeled by 1,950,000 + 0.35x y= . Describe the company's production level so that the average cost of x producing each unit does not exceed $6.85. A) At least 400,000 units
290)
B) At least 300,000 units D) Not more than 400,000 units
C) Not more than 300,000 units
Use the vertex and intercepts to sketch the graph of the quadratic function. 291) f(x) = (x - 1)2 - 4
A)
B)
C)
D)
86
291)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 292) x2 - 4x - 12 0 292)
A) (- , -2] [6, )
B) [6, )
C) [-2, 6]
D) (- , -2]
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 293) f(x) = (x - 2)2 (x2 - 9)
A) origin symmetry
B) y-axis symmetry
C) neither
Find the axis of symmetry of the parabola defined by the given quadratic function. 294) f(x) = x2 - 14x + 3
A) x = -46
B) x = 7
C) x = -7
Determine whether the function is a polynomial function. 295) f(x) = x5 + 4x4 - 2
293)
294) D) x = -14
295)
A) Yes
B) No
Graph the function. 3 296) f(x) = x + 4 x2 - 2x
296)
87
A)
B)
C)
D)
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 297) f(x) = 4x2 - 8x 297)
A) maximum; 1, - 4 C) minimum; 1, - 4
B) minimum; - 1, - 4 D) maximum; - 1, - 4
Solve the problem. 298) You have 144 feet of fencing to enclose a rectangular region. What is the maximum area? A) 1296 square feet B) 20,736 square feet
C) 5184 square feet
D) 1292 square feet
Graph the rational function.
88
298)
299) f(x) =
x4 x2 + 25
299)
A)
B)
C)
D)
89
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 300) f(x) = 3x4 + 7x3 - 5x2 + 5x - 12
300)
A) ±1, ± 2, ± 3, ± 6, ± 12, ± 1 , ± 2 , ± 3 3 3 4
B) ±1, ± 2, ± 3, ± 4, ± 6, ± 12, ± 1 , ± 2 , ± 4 3
3
3
C) ± 1, ± 3, ± 1 , ± 3 , ± 1 , ± 1 , ± 3 , ± 1 , ± 1 2
2
3
4
4
6
12
D) ±1, ± 2, ± 3, ± 4, ± 6, ± 12, ± 1 , ± 3 , ± 1 , ± 1 , ± 3 , ± 1 , ± 1 2
2
3
4
4
6
12
Find the zeros of the polynomial function. 301) f(x) = x3 - 10x2 + 25x
301)
A) x = 0, x = 5 C) x = 1, x = 5
B) x = 0, x = -5, x = 5 D) x = 0, x = -5
Find the domain and range of the quadratic function whose graph is described. 302) The vertex is (-1, 0) and the graph opens down. A) Domain: (- , ) B) Domain: (- , ) Range: [0, ) Range: (- , -1] C) Domain: (- , -1] D) Domain: (- , ) Range: (- , 0] Range: (- , 0]
302)
Determine the maximum possible number of turning points for the graph of the function. 303) f(x) = - x2 - 8x + 15
A) 2
B) 3
C) 1
Divide using long division. 4x3 - 47x - 33
304)
303)
D) 0
304)
x+3
A) 4x2 - 12x - 11
B) 4x2 + 12x - 11
C) 4x2 + 59x + 144
D) 4x2 - 59x + 144
x+3
x+3
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 305) y + 4 = (x - 2)2
A) (- 2, - 4)
B) (4, 2)
C) (4, - 2)
D) (2, - 4)
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 306) x5 - 27x3 + 50x = 0
A) origin symmetry
B) y-axis symmetry
90
305)
C) neither
306)
Solve the problem. 307) The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 710 miles above the earth in 12 hours at a velocity of 22,000 mph, how long would it take a satellite to complete an orbit if it is at 1300 miles above the earth at a velocity of 30,000 mph? (Use 3960 miles as the radius of the earth.) Round your answer to the nearest hundredth of an hour. A) 2.45 hours B) 99.12 hours C) 16.11 hours D) 9.91 hours Graph the rational function. 6 308) f(x) = 2 x + 4x + 4
307)
308)
A)
B)
C)
D)
91
Find the range of the quadratic function. 309) f(x) = 4x2 + 2x - 7
A) [- 1 , ) 4
309)
B) [- 29 , ) 4
C) (- , - 29 ] 4
D) (- , - 1 ] 4
Solve the problem. 310) The revenue achieved by selling x graphing calculators is figured to be x(50 - 0.5x) dollars. The cost of each calculator is $22. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $379.50? A) between 24 and 32 calculators B) between 30 and 40 calculators
C) between 23 and 33 calculators
310)
D) between 25 and 31 calculators
Use the vertex and intercepts to sketch the graph of the quadratic function. 311) y + 1 = (x + 5)2
A)
B)
92
311)
C)
D)
Find the horizontal asymptote, if any, of the graph of the rational function. -20x 312) f(x) = 5x3 + x2 + 1
312)
A) y = -4
B) y = - 1
C) y = 0
D) no horizontal asymptote
4
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 313) f(x) = 3x3 - 17x2 + 18x + 8
A)
4 , -1, 2 3
B)
4 - , -1, -2 3
C)
1 - , 2, 4 3
D)
313) 1 , 2, -4 3
Use the graph of the rational function shown to complete the statement.
314)
314)
As x 0 - , f(x) ? A) -
B) 1
C) -0
93
D) +
Divide using synthetic division. x4 - 3x3 + x2 + 4x - 5
315)
315)
x-1
A) x3 + 2x2 - x + 5 - 2
B) x3 - 2x2 - x + 3 - 2
C) x3 - 2x2 + x + 5 + 4
D) x3 - 2x2 + x + 3 + 4
x-1
x-1
x-1
x-1
Graph the rational function. 316) f(x) = 2x x+3
316)
A)
B)
C)
D)
94
Find the y-intercept of the polynomial function. 317) f(x) = 3x - x3
A) -3
317)
B) 0
C) -1
D) 3
Find the horizontal asymptote, if any, of the graph of the rational function. 318) f(x) = 8x 8x + 8
A) y = 0 C) y = 1
318)
B) y = - 1 D) no horizontal asymptote
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 319) x2 + 5x -6 319)
A) (- , -3]
B) [-3, -2]
C) (- , -3] [-2, )
D) [-2, )
95
320) 18x2 < 17x + 1
A) (- , -1)
320)
1 , 18
B) - 1 , 1 18
C) -1, 1
18
D) - , - 1
18
(1, )
Divide using long division. 321) (15x3 + x2 - 30x - 2) ÷ (5x2 - 10)
A) 3x + 5
B) 3x +
321) 2 2 5x - 10
C) 3x +
-2 2 5x - 10
Solve the problem. 322) If y varies directly as x, and y = 500 when x = 150, find y when x = 60.
A) 1250
B) 18
C) 200
D) 3x + 1 5
322) D) 1 18
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 323) f(x) = -3x3 + 3x2 + 3x + 3
A) rises to the left and falls to the right C) falls to the left and rises to the right
B) rises to the left and rises to the right D) falls to the left and falls to the right
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 324) f(x) = x3 + 10x2 + 33x + 36
A) y-axis symmetry
323)
B) origin symmetry
Graph the polynomial function.
96
C) neither
324)
325) f(x) = (x + 1)2 (x2 - 25)
325)
A)
B)
C)
D)
97
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 326) f(x) = -x2(x + 3)(x2 - 1) 326)
A) 0, crosses the x-axis;
-3, crosses the x-axis; -1, crosses the x-axis; 1, crosses the x-axis B) 0, touches the x-axis and turns around; -3, crosses the x-axis; 1, touches the x-axis and turns around C) 0, touches the x-axis and turns around; -3, crosses the x-axis; -1, crosses the x-axis; 1, crosses the x-axis D) 0, touches the x-axis and turns around; 3, crosses the x-axis; -1, touches the x-axis and turns around; 1, touches the x-axis and turns around
Solve the problem. 327) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 3x2 - 18x + 81. Find the number of automobiles that must be produced to minimize the cost. A) 9 thousand automobiles
B) 54 thousand automobiles D) 3 thousand automobiles
C) 6 thousand automobiles Divide using long division. 328) (-6x3 + 4x2 + 17x + 5) ÷ (3x + 1)
A) x2 - 2x - 5
327)
328)
B) x2 + 2x + 5
C) -2x2 + 5
D) -2x2 + 2x + 5
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 329) 15 - 3x 0 329) 6x + 1
A) - , - 1 or [5, )
B) - 1 , 5
C) [5, )
D) - , - 1 or [5, )
6
6
6
98
If y varies directly as x, find the direct variation equation for the situation. 330) y = 3 when x = 1 5
A) y = 1 x 15
B) y = 1 x
330)
C) y = x + 14
3
5
D) y = 15x
Solve the problem. 331) The total profit function P(x) for a company producing x thousand units is given by P(x) = -2x2 + 28x - 96. Find the values of x for which the company makes a profit. [Hint: The
331)
company makes a profit when P(x) > 0.] A) x is less than 6 thousand units or greater than 8 thousand units
B) x is between 6 thousand units and 8 thousand units C) x is less than 8 thousand units D) x is greater than 6 thousand units 332) A rectangular playground is to be fenced off and divided in two by another fence parallel to one
332)
side of the playground. 576 feet of fencing is used. Find the maximum area of the playground. A) 13,824 ft2 B) 15,552 ft2 C) 10,368 ft2 D) 20,736 ft2
Use the graph of the rational function shown to complete the statement.
333)
333)
As x 0 + , f(x) ? A) -1
B) 1
C) +
Find the slant asymptote, if any, of the graph of the rational function. 3 334) g(x) = x + 4 x2 - 25
A) y = x + 4 C) y = x - 25
B) y = x D) no slant asymptote
99
D) -
334)
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 335) f(x) = 6x4 + 3x3 - 4x2 + 3x - 5
335)
A) ± 1, ± 2, ± 3, ± 6, ± 1 , ± 5 , ± 1 , ± 5 , ± 1 , ± 5 2 2 3 3 6 6 B) ± 1, ± 5, ± 1 , ± 5 , ± 1 , ± 5 , ± 1 , ± 5 2
2
3
3
6
6
C) ± 1, ± 5, ± 1 , ± 2 , ± 3 , ± 6 5
5
5
5
D) ± 1, ± 2, ± 3, ± 6, ± 1 , ± 2 , ± 3 , ± 6 5
5
5
5
Solve.
336) Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function decreasing? A) 10 through 30
336)
B) 10 through 20 and 30 through 50 D) 0 through 30
C) 0 through 10 and 30 through 50
Solve the problem. 337) x varies inversely as v, and x = 21 when v = 9. Find x when v = 27. A) x = 7 B) x = 63 C) x = 81
100
337) D) x = 3
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 338) (x - 7)(x + 4) > 0 338)
A) (-4, 7)
B) (- , -4) (7, )
C) (-4, )
D) (- , -7) (4, )
If y varies directly as x, find the direct variation equation for the situation. 339) y = 9 when x = 27 A) y = 3x B) y = 1 x C) y = x + 18 9
339) D) y = 1 x 3
Solve the problem. 340) A person standing close to the edge on top of a 288-foot building throws a baseball vertically upward. The quadratic function s(t) = -16t2 + 64t + 288 models the ball's height above the ground,
340)
341) The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the
341)
s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary. A) 6.7 seconds B) 1.5 seconds C) 352 seconds D) 2 seconds
temperature and inversely as the volume of the gas. If the pressure is 936 kPa (kiloPascals) when the number of moles is 8, the temperature is 260° Kelvin, and the volume is 960 cc, find the pressure when the number of moles is 10, the temperature is 270° K, and the volume is 600 cc. A) 972 B) 1008 C) 1944 D) 1872
101
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 342) x 342) 2 x+3
A) [-6, -3)
B) (- , -3) or [0, )
C) (-3, 6]
D) (- , -6] or (-3, )
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 343) f(x) = -4x4 + 3x2 - 2x + 6
343)
A) ± 1 , ± 1 , ± 3 , ± 3 , ± 1, ± 2, ± 3, ± 4, ± 6 4 2 4 2
B) ± 1 , ± 1 , ± 1 , ± 2 , ± 4 , ± 1, ± 2, ± 4 6 2 3 3 3
C) ± 1 , ± 1 , ± 3 , ± 3 , ± 1, ± 2, ± 3, ± 6
D) ± 1 , ± 1 , ± 2 , ± 3 , ± 3 , ± 1, ± 2, ± 3, ± 6
4
2
4
2
4
2
3
4
2
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 344) f(x) = 11(x - 5)2 + 4
A) (11, 5)
B) (4, -5)
C) (-5, 4)
D) (5, 4)
Divide using synthetic division. 4x2 - 33x + 54
345)
345)
x-6
A) -9x - 6
344)
B) x - 9
C) 4x - 9
D) -4x + 9
Find the x-intercepts (if any) for the graph of the quadratic function. 346) y + 4 = (x - 2)2
A) (0, 0) C) (0, 0) and (-4, 0)
346)
B) (0, 0) and (4, 0) D) (-4, 0) and (4, 0)
Determine the constant of variation for the stated condition. 347) z varies directly as x and inversely as y, and z = 5 when x = 55 and y = 25. A) k = 25 B) k = 25 C) k = 11 11 25
347) D) k = 5
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 348) f(x) = 8x4 - 7x2 - 2; between 1 and 2 348)
A) f(1) = -1 and f(2) = -98; no C) f(1) = 1 and f(2) = 99; no
B) f(1) = 1 and f(2) = -98; yes D) f(1) = -1 and f(2) = 98; yes
102
Solve the problem. 349) If y varies directly as the cube of x, and y = 10 when x = 4, find y when x = 10. A) 16 B) 25 C) 625 25 4
349) D) 4
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 350) x2 + 6x -8 350)
A) (- , 2] [4, )
B) (2, 4)
C) [2, 4]
D) [-4, -2]
Find an nth degree polynomial function with real coefficients satisfying the given conditions. 351) n = 4; 3, 1 , and 3 + 2i are zeros; f(1) = 32 2
A) f(x) = -4x4 + 38x3 - 142x2 + 218x - 78 C) f(x) = -2x4 + 38x3 - 142x2 + 218x - 78
351)
B) f(x) = -6x4 + 57x3 - 213x2 + 327x - 117 D) f(x) = 2x4 - 19x3 + 71x2 + 218x - 78
Solve the problem. 352) The sum of 81 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition. A) any number between 0 and 1 B) any number greater than 0 9
C) any number greater than 1
D) any number between - 1 and 1
9
9
103
9
352)
The graph of a quadratic function is given. Determine the function's equation.
353)
353)
A) j(x) = (x - 2)2 - 2 C) g(x) = (x + 2)2 - 2
B) f(x) = (x + 2)2 + 2 D) h(x) = (x - 2)2 + 2
Find the y-intercept for the graph of the quadratic function. 354) f(x) = -x2 - 2x + 8
A) (0, 8)
B) (0, -8)
354) C) (0, -4)
Find the zeros of the polynomial function. 355) f(x) = x3 + 2x2 - 9x - 18
D) (8, 0)
355)
A) x = -3, x = 3 C) x = 2, x = -3, x = 3
B) x = -2, x = 9 D) x = -2, x = -3, x = 3
Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. 356) x3 + 9x2 + 26x + 24 = 0 356)
A) -2; The remainder is zero; -2, -3, and 4, or {-3, -2, 4} B) -2; The remainder is zero; -2, 3, and -4, or {-4, -2, 3} C) -2; The remainder is zero; -2, -3, and -4, or {-4, -3, -2} D) -2; The remainder is zero; 2, -3, and -4, or {-4, -3, 2}
104
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 357) x4 + 8x3 - 33x2 = 0 357)
A) 0, touches the x-axis and turns around;
B) 0, touches the x-axis and turns around;
-11, crosses the x-axis; 3, crosses the x-axis C) 0, touches the x-axis and turns around; 11, crosses the x-axis; -3, crosses the x-axis
11, touches the x-axis and turns around; -3, touches the x-axis and turns around D) 0, crosses the x-axis; -11, crosses the x-axis; 3, crosses the x-axis
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 358) x3 - 6x2 + 7x + 2 = 0 358)
A) {2, 2 + 5, 2 - 5} C) {-2, 4 + 5, 4 - 5}
B) {2, 4 + 2, 4 - 2} D) {1, -1, -2}
Find the indicated intercept(s) of the graph of the function. 359) x-intercepts of f(x) = x + 5 x2 + 5x - 3
A) (5, 0)
359)
B) 5 , 0
C) (-5, 0)
3
D) none
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 2 360) f(x) = x + 1 (x - 2)5 360) 5
A) - 1 , multiplicity 2, crosses the x-axis; 5
2, multiplicity 5, touches the x-axis and turns around B) 1 , multiplicity 2, touches the x-axis and turns around; 5 -2, multiplicity 5, crosses the x-axis. C) 1 , multiplicity 2, crosses the x-axis; 5 -2, multiplicity 5, touches the x-axis and turns around D) - 1 , multiplicity 2, touches the x-axis and turns around; 5 2, multiplicity 5, crosses the x-axis.
Solve the problem. 361) A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams per liter after t hours is modeled by 7t C(t) = . 2t2 + 2 Estimate the drug's concentration after 2 hours. (Round to the nearest hundredth.) A) 2.33 milligrams per liter B) 1.40 milligrams per liter
C) 2.44 milligrams per liter
D) 1.51 milligrams per liter
105
361)
Solve.
362) The amount of time it takes a swimmer to swim a race is inversely proportional to the average
362)
speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average speed of the swimmer if it takes 50 seconds to finish the race. A) 3 feet per second B) 2 feet per second
C) 4 feet per second
D) 5 feet per second
Find the domain of the rational function. 363) f(x) = x + 8 x2 - 4x
363)
A) all real numbers C) {x|x -2, x 2}
B) {x|x 0, x 4} D) {x|x -2, x 2, x -8}
Find the vertical asymptotes, if any, of the graph of the rational function. 364) g(x) = x x+3
A) x = 0 and x = -3 C) x = 0 and x = 3
364)
B) x = -3 D) no vertical asymptote
Divide using synthetic division. 365) (5x5 + 12x4 - 7x3 + x2 - x + 50) ÷ (x + 3)
365)
A) 5x4 - 3x3 + 2x2 - 5x - 15 + 8
B) 5x4 - 3x3 + 2x2 - 6x + 15 + 14
C) 5x4 - 3x3 + 2x2 - 6x - 15 + 14
D) 5x4 - 3x3 + 2x2 + 5x + 14 + 8
x+3
x+3
x+3
x+3
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 366) f(x) = x7 + x6 + x2 + x + 4 366)
A) 0 positive zeros, 1 negative zero C) 0 positive zeros, 0 negative zeros
B) 0 positive zeros, 3 or 1 negative zeros D) 0 positive zeros, 2 or 0 negative zeros
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 367) f(x) = x3 - 8x2 - x + 8
A) {1, -1, 8}
B) {1, -1, -8}
C) {-1, 2, -4}
367)
D) {1, 2, 4}
Divide using synthetic division. 6x3 - 26x2 + 6x + 8
368)
368)
x-4
A) 6x2 - 2x - 2
B) -6x2 + 4x - 2
C) -6x2 - 4x + 2
106
D) 3 x2 - 13 x + 3 2
2
2
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 369) f(x) = 4(x + 6)(x + 5)3 369)
A) 6, multiplicity 1, touches x-axis; 5, multiplicity 3, touches x-axis and turns around B) -6, multiplicity 1, crosses x-axis; -5, multiplicity 3, crosses x-axis C) 6, multiplicity 1, crosses x-axis; 5, multiplicity 3, crosses x-axis D) -6, multiplicity 1, crosses x-axis; -5, multiplicity 3, touches x-axis and turns around Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 370) f(x) = x4 - 81x2
A) y-axis symmetry
B) origin symmetry
370)
C) neither
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 371) f(x) = x3 + 6x2 - x - 6 371)
A) -1, multiplicity 1, touches the x-axis and turns around; 1, multiplicity 1, touches the x-axis and turns around; - 6, multiplicity 1, touches the x-axis and turns around B) -1, multiplicity 1, crosses the x-axis; 1, multiplicity 1, crosses the x-axis; - 6, multiplicity 1, crosses the x-axis. C) 1, multiplicity 2, touches the x-axis and turns around; - 6, multiplicity 1, crosses the x-axis. D) 6, multiplicity 1, crosses the x-axis; 1, multiplicity 1, crosses the x-axis; - 6, multiplicity 1, crosses the x-axis.
Solve the problem. 372) For a resistor in a direct current circuit that does not vary its resistance, the power that a resistor must dissipate is directly proportional to the square of the voltage across the resistor. The resistor 1 must dissipate watt of power when the voltage across the resistor is 8 volts. Find the power 16 that the resistor must dissipate when the voltage across it is 16 volts. A) 1 watt B) 1 watt C) 1 watt 4 8 2
372)
D) 4 watts
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 373) x3 - 3x2 - x + 3 = 0 373)
A) {1, -1, -3}
B) {1, -1, 3}
C) {-1, 1, -3}
107
D) {1, 1, 3}
Determine whether the graph shown is the graph of a polynomial function.
374)
374)
A) polynomial function
B) not a polynomial function
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 375) x4 + 3x3 - 15x2 - 45x - 28 = 0 375)
A) {1, -4, -3 + 2, -3 - 2} C) {-1, -4, -3 + 3, -3 - 3}
B) {-1, 5, -3 + 3, -3 - 3} D) {-1, 4, -3 + 2, -3 - 2}
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 376) f(x) = -4x5 - 10x4 - 5x3 + 3x2 + x + 20 376)
A) 1 positive zero, 2 or 0 negative zeros C) 1 positive zero, 3 or 1 negative zeros
B) 1 positive zero, 4 or 2 negative zeros D) 1 positive zero, 4, 3 or 1 negative zeros
Determine the constant of variation for the stated condition. 377) g varies directly as f, and g = 84 when f = 6. A) k = 16 B) k = 1 14
377) C) k = 14
Find the vertical asymptotes, if any, of the graph of the rational function. 378) g(x) = x + 1 x(x - 1)
A) x = -1 and x = 1 C) x = 0 and x = 1
B) x = 1 D) no vertical asymptote
Graph the polynomial function.
108
D) k = 78
378)
379) f(x) = 5x - x3 - x5
379)
A)
B)
C)
D)
Use the vertex and intercepts to sketch the graph of the quadratic function.
109
380) f(x) = -x2 + 4x - 3
380)
A)
B)
C)
D)
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 381) f(x) = 2(x + 1)(x + 2)4 381)
A) -1, multiplicity 1, touches x-axis and turns around; -2, multiplicity 4, crosses x-axis B) 1, multiplicity 1, touches x-axis and turns around; 2, multiplicity 4, crosses x-axis C) 1, multiplicity 1, crosses x-axis; 2, multiplicity 4, touches x-axis and turns around D) -1, multiplicity 1, crosses x-axis; -2, multiplicity 4, touches x-axis and turns around
110
Solve the problem. 382) An object is propelled vertically upward from the top of a 224-foot building. The quadratic function s(t) = -16t2 + 128t + 224 models the ball's height above the ground, s(t), in feet, t seconds
382)
383) In one U.S. city, the quadratic function f(x) = 0.0038x2 - 0.41x + 36.47 models the median, or
383)
after it was thrown. How many seconds does it take until the object finally hits the ground? Round to the nearest tenth of a second if necessary. A) 4 seconds B) 2 seconds C) 1.5 seconds D) 9.5 seconds
average, age, y, at which men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) A) 1954, 47.5 years old B) 1954, 25.4 years old
C) 1936, 47.5 years old
D) 1951, 36 years old
384) The pressure of a gas varies jointly as the amount of the gas (measured in moles) and the
384)
385) A herd of bison is introduced to a wildlife refuge. The number of bison, N(t), after t years is
385)
temperature and inversely as the volume of the gas. If the pressure is 1395 kPa (kiloPascals) when the number of moles is 6, the temperature is 310° Kelvin, and the volume is 480 cc, find the pressure when the number of moles is 7, the temperature is 320° K, and the volume is 420 cc. A) 960 B) 1860 C) 1920 D) 990
described by the polynomial function N(t) = -t4 + 18t + 160. Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the bison population? A) The bison population in the refuge will grow out of control.
B) The bison population in the refuge will be displaced by "oil" wells. C) The bison population in the refuge will die out. D) The bison population in the refuge will reach a constant amount greater than 0. 386) A ball is thrown vertically upward with an initial velocity of 192 feet per second. The distance in
386)
feet of the ball from the ground after t seconds is s = 192t - 16t2 . For what interval of time is the ball more than 432 above the ground? A) between 5.5 and 6.5 seconds B) between 9 and 15 seconds
C) between 3 and 9 seconds
D) between 2.5 and 9.5 seconds
387) You have 340 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. A) 87 ft by 83 ft
387)
B) 85 ft by 85 ft D) 170 ft by 170 ft
C) 170 ft by 42.5 ft
388) Is there origin symmetry for the rational function f(x) = A) Yes
6x ? 2 9x + 10
B) No
111
388)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 389) f(x) = 3x3 - x2 - 18x + 6
A) { 1 , 3
6, -
6}
389)
B) {-3, 6, - 6}
C) {- 1 , 6, - 6}
D) {3, 6, - 6}
3
Use the graph of the rational function shown to complete the statement.
390)
390)
As x + , f(x) ? A) -
B) +
C) -1
D) 1
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 391) f(x) = x4 + 4x3 - 11x2 - 26x - 12
A) {1, -3, -3 + 5, -3 - 5} C) {-1, -3, -3 + 2, -3 - 2}
391)
B) {-1, 3, -3 + 5, -3 - 5} D) {-1, 4, -3 + 2, -3 - 2}
Use the graph of the rational function shown to complete the statement.
392)
392)
As x 3 - , f(x) ? A) -
B) -3
C) +
112
D) 2
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. 393) Touches the x-axis at 0 and crosses the x-axis at 2; lies below the x-axis between 0 and 2. 393) A) f(x) = -x3 + 2x2 B) f(x) = x3 + 2x2
C) f(x) = x3 - 2x2
D) f(x) = -x3 - 2x2
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 394) (x - 1)(3 - x) 0 394) (x - 2)2
A) (- , -3) (-1, )
B) (- , -3] (-2, -1) [1, )
C) (- , 1) (3, )
D) (- , 1] [3, )
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 395) f(x) = -6x3 (x - 4)(x + 5)2
A) falls to the left and falls to the right C) rises to the left and rises to the right
395)
B) falls to the left and rises to the right D) rises to the left and falls to the right
Find the indicated intercept(s) of the graph of the function. 396) x-intercepts of f(x) = (x - 7)(2x + 5) x2 + 2x - 5
396)
A) (7, 0) and (-5, 0)
B) (7, 0) and - 5 , 0
C) (-7, 0) and 5 , 0
D) none
2
2
113
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 397) f(x) = -x3(x + 2)2 (x - 8) 397)
A) 0, crosses the x-axis;
B) 0, touches the x-axis and turns around;
-2, touches the x-axis and turns around; 8, crosses the x-axis C) 0, touches the x-axis and turns around; -2, touches the x-axis and turns around; 8, crosses the x-axis
2, crosses the x-axis; 8, crosses the x-axis D) 0, crosses the x-axis; 2, touches the x-axis and turns around; -8, crosses the x-axis
Find the axis of symmetry of the parabola defined by the given quadratic function. 398) f(x) = -7(x - 3)2 - 8
A) x = 3
B) x = -7
C) x = -3
398) D) x = -8
Solve the problem. 399) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. A measuring device is calibrated to give V = 325 in3 when T = 500° and P = 20 lb/in2 .
399)
What is the volume on this device when the temperature is 170° and the pressure is 25 lb/in2 ? A) V = 6.8 in3 B) V = 88.4 in3 C) V = 108.4 in3 D) V = 68.4 in3
Divide using long division. x4 + 16
400)
400)
x-2
A) x3 + 2x2 + 4x + 8 + 16
B) x3 + 2x2 + 4x + 8
C) x3 + 2x2 + 4x + 8 + 32
D) x3 - 2x2 + 4x - 8 + 32
x-2 x-2
x-2
114
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 401) x < 110 - x2 401)
A) (-10, 11)
B) (- , -11) (10, )
C) (- , 10) (11, )
D) (-11, 10)
Find the range of the quadratic function. 402) f(x) = 11(x - 2)2 + 9
A) [9, )
402)
B) [2, )
C) [-9, )
D) (- , 9]
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 403) f(x) = -x2(x + 6)(x2 - 1)
A) y-axis symmetry
B) origin symmetry
Use synthetic division and the Remainder Theorem to find the indicated function value. 404) f(x) = 2x3 - 7x2 - 5x + 11; f(-3)
B) 57
A) -17
C) -121
404) D) -91
Find the horizontal asymptote, if any, of the graph of the rational function. 3 405) h(x) = 15x 3x2 + 1
A) y = 1
B) y = 0
C) y = 5
D) no horizontal asymptote
5
Find the x-intercepts (if any) for the graph of the quadratic function. 406) f(x) = 2x2 + 14x + 24
A) (3, 0) and (4, 0) C) (-3, 0) and (-4, 0)
B) (3, 0) and (-4, 0) D) (-3, 0) and (4, 0)
115
403)
C) neither
405)
406)
Divide using synthetic division. x5 + x3 - 5
407)
407)
x-2
A) x4 + 2x3 + 5x2 + 10x + 20 + 35
B) x4 + 3 + 1
C) x4 + 3x2 + 1
D) x4 + 2x3 + 4x2 + 9x + 18 + 31
x-2
x-2
x-2
x-2
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 408) (x + 7)(x - 5) 0 408) x-1
A) (- , -7] (1, 5]
B) (- , -7] [5, )
C) [-7, 1] [5, )
D) [-7, 1) [5, )
Solve the problem. 409) The voltage across a resistor is jointly proportional to the resistance of the resistor and the current flowing through the resistor. If the voltage across a resistor is 12 volts for a resistor whose resistance is 2 ohms and when the current flowing through the resistor is 6 amperes, find the voltage across a resistor whose resistance is 5 ohms and when the current flowing through the resistor is 4 amperes. A) 30 volts B) 24 volts C) 8 volts D) 20 volts Determine the maximum possible number of turning points for the graph of the function. 410) f(x) = x7 + 3x8
A) 8
B) 1
C) 3
116
D) 7
409)
410)
Use the graph of the rational function shown to complete the statement.
411)
411)
As x 3 + , f(x) ? A) -
C) 3
B) +
Determine whether the function is a polynomial function. 412) f(x) = 3 - 2 x3
D) 0
412)
A) No
B) Yes
Use the vertex and intercepts to sketch the graph of the quadratic function. 413) f(x) = x2 + 6x + 8
A)
B)
117
413)
C)
D)
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 414) f(x) = x5 - 6x2 + 3x + 3
B) ± 1, ± 1 3
A) ± 1, ± 3
C) ± 3, ± 1 3
414) D) ± 1 , ± 1 , ± 3 6 2
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 415) f(x) = x2 + 2
A) (0, 2)
B) (0, -2)
C) (-2, 0)
Find the slant asymptote, if any, of the graph of the rational function. 2 416) f(x) = x + 4x - 4 x-4
A) y = x + 8 C) y = x + 4
416)
B) y = x D) no slant asymptote
Divide using synthetic division. 417) (x2 + 16x + 61) ÷ (x + 7)
A) x + 10
417) B) x + 9 - 2 x+7
C) x + 9 x+7
D) x + 9 + 2 x+7
Use the Rational Zero Theorem to list all possible rational zeros for the given function. 418) f(x) = 6x4 + 3x3 - 2x2 + 2
A) ± 1 , ± 1 , ± 1 , ± 1, ± 2 6 3 2
B) ± 1 , ± 1 , ± 1 , ± 2 , ± 1, ± 2, ± 3 6 3 2 3
C) ± 1 , ± 1 , ± 1 , ± 2 , ± 1, ± 2
D) ± 1 , ± 3 , ± 1, ± 2, ± 3, ± 6
6
3
415)
D) (2, 0)
2
3
2
418)
2
Solve the problem.
419) f varies jointly as q2 and h, and f = 96 when q = 4 and h = 3. Find f when q = 2 and h = 6. A) f = 24 B) f = 12 C) f = 48 D) f = 8
118
419)
420) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = -7x2 , but which has a maximum of 9 at x = 5.
A) f(x) = 7(x - 5)2 + 9 C) f(x) = -7(x - 5)2 - 9
B) f(x) = -7(x + 5)2 + 9 D) f(x) = -7(x - 5)2 + 9
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 421) f(x) = x3 (x + 2)(x + 5)2
A) falls to the left and falls to the right C) rises to the left and falls to the right
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 423) f(x) = 8x2 - x3
B) y-axis symmetry
422)
423)
C) neither
Find the range of the quadratic function. 424) y + 9 = (x + 3)2
A) [- 9, )
421)
B) falls to the left and rises to the right D) rises to the left and rises to the right
Write an equation that expresses the relationship. Use k for the constant of proportionality. 422) p varies jointly as q and r and inversely as the square root of a. A) p = qr B) p = kqr C) p = kq D) p = k(q + r) k a a r a a
A) origin symmetry
420)
424)
B) (- , 9]
C) (- , 3]
119
D) [9, )
Graph the polynomial function. 425) f(x) = -x2(x - 4)(x - 1)
425)
A)
B)
C)
D)
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 426) f(x) = 8 - (x + 5)2
A) (5, 8)
B) (8, 5)
C) (-5, 8)
Graph the polynomial function.
120
D) (8, -5)
426)
427) f(x) = 6x4 + 9x3
427)
A)
B)
C)
D)
Find the horizontal asymptote, if any, of the graph of the rational function. 428) f(x) = 4x 2x2 + 1
A) y = 1
B) y = 2
C) y = 0
D) no horizontal asymptote
2
121
428)
Find the range of the quadratic function. 429) f(x) = (x + 2)2 + 8
A) [2, )
429)
B) [-2, )
C) [8, )
D) [-8, )
Use the graph of the rational function shown to complete the statement.
430)
430)
As x - , f(x) ? A) 0
B) -
C) +
D) -1
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 431) (x + 5)(x + 2)(x - 4) > 0 431)
A) (4, )
B) (- , -5) (-2, 4)
C) (-5, -2) (4, )
D) (- , -2)
122
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. 432) 2x3 - 13x2 + 17x + 12 = 0; 3 432)
A) - 1 , 4, 3 2
B) - 1 , -4, 3
C) 1 , 4, 3
2
2
Find the variation equation for the variation statement. 433) c varies directly as a and inversely as b; c = 2 when a = 26 and b = 78 A) c = a B) c = 6 C) c = 6ab 6b ab Graph the rational function. 2 434) f(x) = 2x x2 - 25
D) 2, -1, 3
433) D) c = 6a b
434)
A)
B)
123
C)
D)
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 435) f(x) = -x2(x + 6)(x2 + 1) 435)
A) 0, touches the x-axis and turns around;
B) 0, touches the x-axis and turns around;
-6, crosses the x-axis; -1, crosses the x-axis; 1, crosses the x-axis; D) 0, touches the x-axis and turns around; 6, crosses the x-axis
-6, crosses the x-axis
C) 0, touches the x-axis and turns around;
-6, crosses the x-axis; -1, touches the x-axis and turns around
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 436) f(x) = 1 x4(x2 - 3)(x - 7) 436) 4
A) 0, multiplicity 4, touches x-axis and turns around; 7, multiplicity 1, crosses x-axis
B) 0, multiplicity 4, touches x-axis and turns around;
7, multiplicity 1, crosses x-axis 3, multiplicity 2, touches x-axis and turns around C) 0, multiplicity 4, crosses x-axis; 7, multiplicity 1, touches x-axis and turns around; 3, multiplicity 1, touches x-axis and turns around; - 3, multiplicity 1, touches x-axis and turns around D) 0, multiplicity 4, touches x-axis and turns around; 7, multiplicity 1, crosses x-axis; 3, multiplicity 1, crosses x-axis; - 3, multiplicity 1, crosses x-axis
124
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 437) x5 - 28x3 + 75x = 0 437)
A) 0, crosses the x-axis;
B) 0, touches the x-axis and turns around;
5, crosses the x-axis; -5, crosses the x-axis; 3, crosses the x-axis; - 3, crosses the x-axis C) 0, touches the x-axis and turns around; 25, touches the x-axis and turns around; 3, touches the x-axis and turns around
5, crosses the x-axis; -5, crosses the x-axis; 3, crosses the x-axis; - 3, crosses the x-axis D) 0, crosses the x-axis; 25, touches the x-axis and turns around; 3, touches the x-axis and turns around
Find the domain of the rational function. 438) g(x) = 2x x-1
438)
A) {x|x -1} C) {x|x 0}
B) {x|x 1} D) all real numbers
Solve.
439) Suppose that a polynomial function is used to model the data shown in the graph below.
For what intervals is the function decreasing? A) 0 through 10 and 25 through 40
439)
B) 10 through 50 D) 10 through 25 and 40 through 45
C) 10 through 25 and 40 through 50
Write an equation that expresses the relationship. Use k for the constant of proportionality. 440) r varies directly as a and inversely as the difference between s and t. A) r = a B) r = ka(s - t) C) r = ka D) r = k k(s - t) s- t a(s - t)
125
440)
Use the graph of the rational function shown to complete the statement.
441)
441)
As x 3 - , f(x) ? A) -3
B) 0
C) -
D) +
Determine the maximum possible number of turning points for the graph of the function. 442) f(x) = x4 ( x4 + 2)(6x + 4)
A) 8
B) 4
C) 48
Divide using long division. 443) (4x5 - x3 + 5x2 - 89x - 25) ÷ (x2 - 5)
442)
D) 9
443)
A) 4x3 + 19x + 5 + 6x
B) 4x3 + 19x + 5 + 6x - 50
C) 4x3 + 19x - 5 + 6x
D) 4x3 + 19x + 5 - 6x
x2 - 5
x2 - 5
x2 - 5
x2 - 5
126
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 444) x - 2 > 0 444) x+5
A) (- , -5)
B) (- , -5) or (2, )
C) (-5, 2)
D) (2, )
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 445) x2 - 3x - 28 < 0 445)
A) (- , -4) (7, )
B) (7, )
C) (- , -4)
D) (-4, 7)
127
Find the x-intercepts (if any) for the graph of the quadratic function. 446) f(x) = 2x2 + 15x + 28
A) (-7, 0) and (-2, 0) C) (-7, 0) and (2, 0)
446)
B) (-4, 0) and (3.5, 0) D) (-4, 0) and (-3.5, 0)
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 447) x + 7 < 3 447) x+8
A) (-8, - 17 ) 2
B) (- , -8) or (- 17 , ) 2
C)
D) (- , - 17 ) or (8, ) 2
Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 448) f(x) = 5x3 - 7x + 7; between -2 and -1 448)
A) f(-2) = 19 and f(-1) = 9; no C) f(-2) = 19 and f(-1) = -9; yes
B) f(-2) = -19 and f(-1) = -9; no D) f(-2) = -19 and f(-1) = 9; yes
Find the zeros of the polynomial function. 449) f(x) = x3 + 9x2 - x - 9
449)
A) x = 1, x = - 9, x = 9 C) x = - 9, x = 9
B) x = -1, x = 1, x = - 9 D) x = 81
128
The graph of a quadratic function is given. Determine the function's equation.
450)
450)
A) g(x) = (x + 2)2 - 2 C) f(x) = (x + 2)2 + 2
B) h(x) = (x - 2)2 + 2 D) j(x) = (x - 2)2 - 2
Determine the maximum possible number of turning points for the graph of the function. 451) f(x) = (x + 7)(x + 1)(5x + 4) A) 0 B) 3 C) 5 D) 2 Find the y-intercept of the polynomial function. 452) f(x) = (x - 3)2 (x2 - 25)
A) 75
451)
452)
B) -225
C) -75
Solve the problem. 453) y varies directly as z and y = 270 when z = 15. Find y when z = 14. A) 196 B) 324 C) 252 Use the vertex and intercepts to sketch the graph of the quadratic function. 454) f(x) = -2(x + 1)2 + 3
129
D) 225
453) D) 225
454)
A)
B)
C)
D)
Find the domain of the rational function. 455) h(x) = x + 7 x2 + 64
455)
A) {x|x -8, x 8} C) {x|x -8, x 8, x -7}
B) all real numbers D) {x|x 0, x -64}
Use the graph of the rational function shown to complete the statement.
456)
456)
As x -2 - , f(x) ? A) 0
C) 2
B) +
130
D) -
Find the indicated intercept(s) of the graph of the function. 457) x-intercepts of f(x) = x - 9 x2 + 7x - 3
A) (3, 0)
457)
B) (9, 0)
C) (7, 0)
D) none
B) 9x + 1
C) 9x - 1
D) x - 62
Divide using long division. 458) (9x2 - 62x - 7) ÷ (x - 7)
A) 9x2 + 62
458)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 459) (x + 7)(x - 4) 0 459)
A) (-7, 4)
B) (- , -7) (4, )
C) (- , -7] [4, )
D) [-7, 4]
Find the y-intercept for the graph of the quadratic function. 460) f(x) = 6 + 5x + x2
A) (0, -6)
B) (0, 6)
460) C) (0, 5)
D) (0, 3)
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. 461) 2x3 - 5x2 - 21x + 36 = 0; 4 461)
A) 3 , -3, 4 2
B) - 3 , 3, 4
C) 3 , 3, 4
2
2
131
D) - 3 , -3, 4 2
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 462) x3 - 5x2 + 17x - 13 = 0 462)
A) {1, 3 + 5, 3 - 5} C) {1, 3 + 2i, 3 - 2i}
B) {1, 2 + 3i, 2 - 3i} D) {-1, 2 + 5, 4 - 5}
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 463) 19x2 - 5x 0 463)
A) (- , 0]
5 , 19
B) 0, 5
19
C) 0, 19 5
D) - 5 , 0 19
Find an nth degree polynomial function with real coefficients satisfying the given conditions. 464) n = 3; 3 and i are zeros; f(2) = 15 A) f(x) = 3x3 - 9x2 - 3x + 9 B) f(x) = 3x3 - 9x2 + 3x - 9
C) f(x) = -3x3 + 9x2 + 3x - 9
D) f(x) = -3x3 + 9x2 - 3x + 9
Find the range of the quadratic function. 465) f(x) = x2 + 12x + 9
A) (- , -27]
464)
465)
B) (- , -99]
C) [6, )
132
D) [-27, )
Solve the problem. 466) The rational function 125x C(x) = , 0 x < 100 100 - x
466)
describes the cost, C, in millions of dollars, to inoculate x% of the population against a particular strain of the flu. Determine the difference in cost between inoculating 75% of the population and inoculating 50% of the population. (Round to the nearest tenth, if necessary.) A) $0.8 million B) $250.1 million C) $0.9 million D) $250.0 million
Write an equation that expresses the relationship. Use k as the constant of variation. 467) x varies jointly as s and t. A) x = kskt B) x = kt C) x = kst s
467) D) x = ks t
Solve the problem.
468) The width of a rectangle is x - 3 feet and its area is 4x3 + 21x2 + 14x - 24 square feet. Write a 4
468)
polynomial that represents the length of the rectangle.
A) 4x2 + 24x + 32 ft
B) 4x2 + 18x + 1 ft
C) 4x2 - 24x + 32 ft
D) 4x2 + 24x - 32 ft
2
Find the axis of symmetry of the parabola defined by the given quadratic function. 469) y + 4 = (x + 2)2
A) x = 2
B) y = 4
C) x = - 2
469) D) y = -4
The graph of a quadratic function is given. Determine the function's equation.
470)
470)
A) j(x) = -x2 + 2 C) h(x) = -x2 - 2
B) f(x) = -x2 - 4x - 4 D) g(x) = -x2 + 4x + 4
133
Write an equation that expresses the relationship. Use k as the constant of variation. 471) The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 63 ft from a light is 2.9 foot-candles, find the intensity on a screen 90 ft from the light. A) 1.421 foot-candles B) 5.92 foot-candles
C) 4.14 foot-candles
471)
D) 2.03 foot-candles
Solve the problem. 472) The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 14 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 5 hours. A) 35 gallons B) 42 gallons C) 10 gallons D) 40 gallons Graph the polynomial function. 473) f(x) = -2x3 (x - 3)2 (x + 1)
472)
473)
A)
B)
134
C)
D)
Solve the problem. 474) If y varies directly as the square root of x, and y = 10 when x = 25, find y when x = 16. A) 25 B) 125 C) 8 D) 32 2 8 5
474)
If y varies inversely as x, find the inverse variation equation for the situation. 475) y = 1 when x = 15 3
A) y = 1 x 45
Divide using long division. 476) (x2 - 12x + 35) ÷ (x - 7)
A) x - 5
B) y = x
C) y = 1
B) x2 - 12
C) x2 - 5
5
5x
475) D) y = 5
x
476) D) x - 12
If y varies inversely as x, find the inverse variation equation for the situation. 477) y = 30 when x = 1 6
A) y = x
B) y = 5
5
C) y = 180x
x
477) D) y = 1
Find the horizontal asymptote, if any, of the graph of the rational function. 478) f(x) = -4x - 7 5x + 6
A) y = - 7
B) y = - 4
C) y = -4
D) no horizontal asymptote
6
5
135
5x
478)
Solve the problem. 479) Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual is underweight or overweight. BMI varies directly as one's weight, in pounds, and inversely as the square of one's height, in inches. In adults, normal values for the BMI are between 20 and 25. A person who weighs 180 pounds and is 72 inches tall has a BMI of 24.41. What is the BMI, to the nearest tenth, for a person who weighs 125 pounds and who is 63 inches tall? A) 21.7 B) 21.4 C) 22.1 D) 22.5 Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. 480) f(x) = (x + 1)(x - 4)(x - 1)2
A) y-axis symmetry
B) origin symmetry
481)
B) [0, )
C) (- , 1]
D) [-1, )
Divide using long division. 482) (28x2 - 27x + 5) ÷ (-4x + 1)
A) x + 5
480)
C) neither
Find the range of the quadratic function. 481) f(x) = x2 + 1
A) [1, )
479)
482) B) 5x + 1
C) -7x + 5
D) 28x + 5
Find the vertical asymptotes, if any, of the graph of the rational function. 483) h(x) = x + 2 x2 - 4
A) x = 2, x = -2 C) x = 2
483)
B) x = -2 D) no vertical asymptote
Solve the problem. 484) The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 88.2 meters in 3 seconds. Find the distance the object falls in 5 seconds. A) 49 meters B) 245 meters C) 15 meters D) 147 meters Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 485) f(x) = -3x4 - 2x3 + 2x2 + 3x + 5
A) rises to the left and rises to the right C) falls to the left and falls to the right
484)
485)
B) rises to the left and falls to the right D) falls to the left and rises to the right
Find the x-intercepts (if any) for the graph of the quadratic function. 486) f(x) = x2 - 1
A) No x-intercepts C) (-1, 0) and (1, 0)
B) (-1, 0) D) (1, 0)
136
486)
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 487) f(x) = 6x6 - 10x5 + x4 - 3x3 + 20 487)
A) 4, 2 or 0 positive zeros, 1 negative zeros B) 4 or 2 positive zeros, no negative zeros C) 4 positive zeros, no negative zeros D) 4, 2 or 0 positive zeros, no negative zeros Find the range of the quadratic function. 488) f(x) = -x2 - 6x + 6
A) (- , -3]
488)
B) (- , 15]
C) [15, )
D) [-3, )
Determine whether the graph shown is the graph of a polynomial function.
489)
489)
A) polynomial function
B) not a polynomial function
Solve the problem.
490) f varies jointly as q2 and h, and f = 54 when q = 3 and h = 2. Find h when f = 288 and q = 4. A) h = 3 B) h = 2 C) h = 6 D) h = 4
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 491) f(x) = x3 + 2x2 - 9x - 18
A) {-2}
B) {-3, -2, 3}
C) {-3, 2, 3}
D) {-3}
C) (- , 2]
D) (- , - 1]
Find the range of the quadratic function. 492) f(x) = -2x2 - 4x
A) (- , 1]
490)
491)
492)
B) (- , - 2]
137
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 493) f(x) = 4 x + 2 (x - 2)3 493)
A) - 2, multiplicity 1, crosses x-axis; 2, multiplicity 3, crosses x-axis B) 2, multiplicity 1, crosses x-axis; -2, multiplicity 3, crosses x-axis C) 2, multiplicity 1, touches the x-axis and turns around; -2, multiplicity 3, touches x-axis and turns around D) - 2, multiplicity 1, touches the x-axis and turns around; 2, multiplicity 3, touches x-axis and turns around
Determine whether the function is a polynomial function. 494) f(x) = x4/3 - x6 + 9
494)
A) Yes
B) No
If y varies directly as x, find the direct variation equation for the situation. 495) y = 12 when x = 20 A) y = 3 x B) y = x - 8 C) y = 4x 5
495) D) y = 5 x 3
Find the degree of the polynomial function. 496) f(x) = x4 + 9x3 - 2
A) 1
496)
B) 3
D) 4
C)
Determine whether the function is a polynomial function. 4 497) f(x) = 7 - x 6
497)
A) No
B) Yes
Divide using long division. 8u4 + 12u3 - 2u
498)
498)
2u2 + u
A) 4u2 + 4u - 2 C) 4u2 + 8u + 4 +
2u 2u2 + u
B) 4u2 + 6u -
2u 2u2 + u
D) 4u2 + 4u -
6u 2u2 + u
Solve the problem. 499) The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x) = 2x2 - 20x + 570, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. A) $470 B) $520
C) $370
Graph the polynomial function.
138
D) $620
499)
500) f(x) = x5 - 6x3 - 16x
500)
A)
B)
C)
D)
139
The graph of a quadratic function is given. Determine the function's equation.
501)
501)
A) h(x) = x2 - 1 C) f(x) = x2 - 2x + 1
B) g(x) = x2 + 2x + 1 D) j(x) = x2 + 1
Graph the rational function. 502) f(x) = 4x x2 - 36
502)
A)
B)
140
C)
D)
Divide using long division. 503) (2x4 - 7x2 + 14x3 - 49x) ÷ (2x + 14)
503)
A) x3 - 7 x
B) x3 - 14x +
C) x3 + 7 x
D) x3 - 7 x - 98x
2 2
2
4x 2x + 14 2x + 14
Determine the constant of variation for the stated condition. 504) h varies jointly as f and g, and h = 56 when f = 35, and g = 40.
A) k = 25
C) k = 1 25
B) k = 40
504) D) k = 1 40
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 505) f(x) = -6x9 + x5 - x2 + 8 505)
A) 3 or 1 positive zeros, 2 or 0 negative zeros B) 2 or 0 positive zeros, 2 or 0 negative zeros C) 3 or 1 positive zeros, 3 or 1 negative zeros D) 2 or 0 positive zeros, 3 or 1 negative zeros Find the degree of the polynomial function. 506) h(x) = -6x + 9 A) 1 B) 0
506) C) -6
D) 2
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 507) f(x) = x3 - 5x2 - 2x + 1
A) rises to the left and falls to the right C) falls to the left and rises to the right
507)
B) rises to the left and rises to the right D) falls to the left and falls to the right
Write an equation that expresses the relationship. Use k as the constant of variation. 508) r varies jointly as the square of s and the square of t. A) r = k + s2 + t2 B) rs2 t2 = k C) r = ks2 t2
141
508) D) r + s2 + t2 = k
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 509) f(x) = 2x4 + 4x3 + 2x2 - 5x - 2
A) falls to the left and falls to the right C) falls to the left and rises to the right
509)
B) rises to the left and rises to the right D) rises to the left and falls to the right
Determine whether the graph shown is the graph of a polynomial function.
510)
510)
A) not a polynomial function
B) polynomial function
Determine the constant of variation for the stated condition. 511) c varies jointly as a and b, and c = 48 when a = 24 and b = 8. A) k = 8 B) k = 1 C) k = 4 8
511) D) k = 1 4
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
512)
512)
A) y-axis symmetry
B) origin symmetry
Graph the function.
142
C) neither
2
513) f(x) = x + 4x - 6
513)
x-9
A)
B)
C)
D)
143
2
514) f(x) = x + 9
514)
x
A)
B)
C)
D)
Solve the problem. 515) The revenue achieved by selling x graphing calculators is figured to be x(49 - 0.2x) dollars. The cost of each calculator is $21. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $975.00? A) between 67 and 73 calculators B) between 65 and 75 calculators
C) between 66 and 64 calculators
D) between 30 and 40 calculators
144
515)
Find a rational zero of the polynomial function and use it to find all the zeros of the function. 516) f(x) = x3 + 8x2 + 14x + 4
Find the coordinates of the vertex for the parabola defined by the given quadratic function. 517) f(x) = -7(x - 3)2 - 4
A) (3, -4)
516)
B) {-2, -6 + 4, -6 - 4} D) {-2, -3 + 7, -3 - 7}
A) {1, -1, -4} C) {2, -6 + 7, -6 - 7}
B) (-4, 3)
C) (-7, -3)
517)
D) (-3, -4)
Solve the problem. 518) The concentration, in parts per million, of a particular drug in a patient's blood x hours after the drug is administered is given by the function
518)
f(x) = -x4 + 11x3 - 41x 2 + 55x How many hours after the drug is administered will it be eliminated from the bloodstream. A) 4 hours B) 16 hours C) 11 hours D) 5 hours
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 519) f(x) = 4x3 - 2x2 + 5x - 5
A) rises to the left and falls to the right C) falls to the left and rises to the right Find the degree of the polynomial function. 520) g(x) = 17x6 - 8
A) 17
520)
B) 7
C) 0
D) 6
Write an equation that expresses the relationship. Use k for the constant of proportionality. 521) p varies directly as q and inversely as r. A) p = kq B) p + q - r = k C) p = kr D) pqr = k r q Determine the maximum possible number of turning points for the graph of the function. 522) g(x) = 4x + 4 A) 1 B) 3 C) 0 D) 2 Find the degree of the polynomial function. 523) f(x) = -16x3 - 7x2 - 1
A) 3
519)
B) falls to the left and falls to the right D) rises to the left and rises to the right
521)
522)
523)
B) 6
C) -16
145
D) -7
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 524) 1 < 1 524) x-2
A) (- , 2] or [3, )
B) (- , 2)
C) (- , 2) or (3, )
D) (2, 3)
Graph the rational function. 525) f(x) = - 3 x2 - 9
525)
A)
B)
146
C)
D)
The graph of a quadratic function is given. Determine the function's equation.
526)
526)
A) g(x) = (x + 2)2 - 2 C) h(x) = (x - 2)2 + 2
B) f(x) = (x + 2)2 + 2 D) j(x) = (x - 2)2 - 2
Find the domain and range of the quadratic function whose graph is described. 527) The maximum is 4 at x = 1 A) Domain: (- , ) B) Domain: (- , 1] Range: [4, ) Range: (- , 4] C) Domain: (- , ) D) Domain: (- , ) Range: (- , 4] Range: (- , 1]
147
527)
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
528)
528)
A) origin symmetry
B) y-axis symmetry
C) neither
Solve the problem. 529) While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If a passenger experiences a force of 32.4 newtons when the car is moving at a speed of 30 kilometers per hour and the passenger has a mass of 40 kilograms, find the force a passenger experiences when the car is moving at 50 kilometers per hour and the passenger has a mass of 50 kilograms. A) 125 newtons B) 150 newtons C) 112.5 newtons D) 100 newtons Graph the polynomial function. 530) f(x) = x3 + 7x2 - x - 7
529)
530)
148
A)
B)
C)
D)
Determine the constant of variation for the stated condition. 531) g varies directly as f, and g = 5 when f = 70. A) k = 1 B) k = 14 14
531) C) k = 15
D) k = 65
Determine whether the function is a polynomial function. 532) f(x) = 5x7 - x5 + 3 x 2
532)
A) No
B) Yes
Find the horizontal asymptote, if any, of the graph of the rational function. 2 533) g(x) = 8x - 2x - 3 9x2 - 5x + 3
A) y = 0
B) y = 2
C) y = 8
D) no horizontal asymptote
5
9
149
533)
Solve the problem. 534) A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, C(t), in milligrams after t hours is modeled by 5t C(t) = . 2 2t + 2
534)
What is the horizontal asymptote for this function? Describe what this means in practical terms. A) y = 0; 0 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream. B) y = 2.50; 2.50 is the final amount, in milligrams, of the drug that will be left in the patient's bloodstream. C) y = 2.50; After 2.50 hours, the concentration of the drug is at its greatest.
D) y = 1.25; After 1.25 hours, the concentration of the drug is at its greatest. Find the range of the quadratic function. 535) f(x) = -7(x - 3)2 - 7
A) [-3, )
535)
B) (- , -7]
C) [-7, )
150
D) (- , 3]
Answer Key Testname: CH 3
1) D 2) C 3) A 4) C 5) D 6) A 7) (a) falls to the left and rises to the right
(b) x-intercepts: (0, 0), touches x-axis and turns; (-2, 0), crosses x-axis (c) y-intercept: (0, 0) (d)
8) (a) falls to the left and to the right
(b) x-intercepts: (-2, 0), crosses x-axis; (3, 0), crosses x-axis (c) y-intercept: (0, 48) (d)
151
Answer Key Testname: CH 3
9) (a) falls to the left and rises to the right
(b) x-intercepts: (1, 0), touches x-axis and turns; (-2, 0), crosses x-axis (c) y-intercept: (0, 2) (d)
10) D 11) B 12) D 13) B 14) B 15) B 16) B 17) B 18) C 19) A 20) B 21) A 22) A 23) D 24) D 25) D 26) D 27) D 28) B 29) D 30) A 31) C 32) C 33) D 34) D 35) B 152
Answer Key Testname: CH 3
36) D 37) A 38) D 39) D 40) B 41) A 42) C 43) B 44) C 45) B 46) B 47) A 48) C 49) C 50) C 51) A 52) A 53) A 54) B 55) A 56) B 57) A 58) B 59) B 60) D 61) A 62) D 63) D 64) A 65) B 66) D 67) C 68) C 69) D 70) C 71) D 72) B 73) C 74) C 75) D 76) A 77) B 153
Answer Key Testname: CH 3
78) B 79) D 80) D 81) B 82) A 83) D 84) D 85) B 86) A 87) B 88) D 89) C 90) B 91) A 92) D 93) D 94) B 95) A 96) C 97) D 98) D 99) A 100) D 101) D 102) A 103) C 104) A 105) B 106) D 107) A 108) B 109) D 110) D 111) A 112) C 113) C 114) B 115) C 116) B 117) C 118) A 119) D 154
Answer Key Testname: CH 3
120) D 121) A 122) D 123) C 124) A 125) D 126) D 127) C 128) B 129) D 130) B 131) A 132) C 133) C 134) D 135) A 136) A 137) A 138) C 139) C 140) B 141) C 142) B 143) D 144) B 145) D 146) D 147) A 148) C 149) D 150) A 151) A 152) B 153) C 154) B 155) B 156) B 157) D 158) B 159) C 160) D 161) C 155
Answer Key Testname: CH 3
162) D 163) D 164) C 165) C 166) D 167) B 168) D 169) A 170) C 171) B 172) A 173) D 174) B 175) C 176) A 177) C 178) A 179) B 180) B 181) B 182) A 183) C 184) A 185) B 186) C 187) D 188) A 189) B 190) C 191) B 192) D 193) B 194) A 195) D 196) C 197) D 198) A 199) D 200) B 201) D 202) C 203) A 156
Answer Key Testname: CH 3
204) B 205) B 206) B 207) B 208) B 209) D 210) D 211) C 212) C 213) B 214) A 215) B 216) B 217) B 218) A 219) C 220) B 221) A 222) B 223) D 224) C 225) A 226) B 227) A 228) B 229) C 230) D 231) C 232) D 233) C 234) C 235) B 236) B 237) B 238) A 239) C 240) A 241) C 242) C 243) D 244) A 245) A 157
Answer Key Testname: CH 3
246) D 247) B 248) A 249) C 250) C 251) A 252) C 253) C 254) D 255) D 256) C 257) A 258) C 259) D 260) C 261) D 262) D 263) D 264) D 265) B 266) C 267) B 268) D 269) D 270) C 271) A 272) B 273) B 274) C 275) D 276) D 277) A 278) C 279) B 280) B 281) D 282) C 283) D 284) B 285) B 286) D 287) B 158
Answer Key Testname: CH 3
288) B 289) B 290) B 291) C 292) C 293) C 294) B 295) A 296) C 297) C 298) A 299) D 300) B 301) A 302) D 303) C 304) A 305) D 306) A 307) D 308) C 309) B 310) C 311) A 312) C 313) C 314) A 315) B 316) B 317) B 318) C 319) C 320) B 321) D 322) C 323) A 324) C 325) B 326) C 327) D 328) D 329) A 159
Answer Key Testname: CH 3
330) D 331) B 332) A 333) C 334) B 335) B 336) A 337) A 338) B 339) D 340) D 341) C 342) A 343) C 344) D 345) C 346) B 347) A 348) D 349) C 350) D 351) A 352) B 353) D 354) A 355) D 356) C 357) A 358) A 359) C 360) D 361) B 362) A 363) B 364) B 365) D 366) B 367) A 368) A 369) B 370) A 371) B 160
Answer Key Testname: CH 3
372) A 373) B 374) A 375) D 376) D 377) C 378) C 379) D 380) D 381) D 382) D 383) B 384) C 385) C 386) C 387) B 388) A 389) A 390) D 391) B 392) A 393) C 394) D 395) A 396) B 397) A 398) A 399) B 400) C 401) D 402) A 403) C 404) D 405) D 406) C 407) A 408) D 409) D 410) D 411) A 412) A 413) C 161
Answer Key Testname: CH 3
414) A 415) A 416) A 417) B 418) C 419) C 420) D 421) D 422) B 423) C 424) A 425) A 426) C 427) B 428) C 429) C 430) A 431) C 432) A 433) D 434) D 435) A 436) D 437) A 438) B 439) C 440) C 441) C 442) A 443) A 444) B 445) D 446) D 447) B 448) D 449) B 450) D 451) D 452) B 453) C 454) A 455) B 162
Answer Key Testname: CH 3
456) B 457) B 458) B 459) D 460) B 461) A 462) B 463) B 464) D 465) D 466) D 467) C 468) A 469) C 470) C 471) A 472) A 473) C 474) C 475) D 476) A 477) B 478) B 479) C 480) C 481) A 482) C 483) C 484) B 485) C 486) C 487) D 488) B 489) B 490) C 491) B 492) C 493) A 494) B 495) A 496) D 497) B 163
Answer Key Testname: CH 3
498) A 499) B 500) C 501) C 502) B 503) A 504) C 505) A 506) A 507) C 508) C 509) B 510) B 511) D 512) B 513) B 514) D 515) B 516) D 517) A 518) D 519) C 520) D 521) A 522) C 523) A 524) C 525) D 526) B 527) C 528) C 529) C 530) A 531) A 532) B 533) C 534) A 535) B
164