CHAPTER 1
Exam Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequality and graph. Express your answer in interval notation. 1) 4x - 4 > 3x - 1
1)
A) [3, ∞) -3 -2 -1
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
8
9
B) (3, ∞) -3 -2 -1
C) (-5, ∞)
D) (-∞, 3] -3 -2 -1
0
1
2
3
4
5
6
7
Provide an appropriate response. 2) Write the equation of a line that passes through (-1, 4) and (5, -1). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0. A) 5x + 6y = 19 B) 5x + 6y = -19 C) 5x - 6y = 19 D) -5x + 6y = 19 3) Find the slope of the line 3x + 4y = 11. 3 A) B) - 3 4 4
3) C) - 4 3
Graph the linear equation and determine its slope, if it exists. 4) 2x - 5y = 20 10
y
8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
2)
8 10 x
-4 -6 -8 -10
1
D) 0
4)
A) slope = 2 5
B) slope = - 2 5 y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2 -2
2
4
6
8 10 x
-10 -8 -6 -4 -2 -2
-4
-4
-6
-6
-8
-8
-10
-10
C) slope = - 2 5 y
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2 -2
2
4
6
8 10 x
-10 -8 -6 -4 -2 -2
-4
-4
-6
-6
-8
-8
-10
-10
Solve the inequality and graph. Express your answer in interval notation. 5) -29 ≤ -4x - 1 ≤ -13
A) (3, 7) 0
1
2
3
4
5
6
7
8
9 10 11
B) [-7, -3] -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
C) [3, 7] -1
0
2
4
6
8 10 x
2
4
6
8 10 x
D) slope = 2 5 10
-1
y
1
2
3
4
5
6
7
8
9 10 11
D) (-7, -3) -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
y
5)
Determine whether the slope of the line is positive, negative, zero, or undefined. 6)
6)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) zero
B) undefined
C) negative
Solve the inequality and graph. Express your answer in interval notation. 7) -3(3x - 2) < -12x - 21
A) (-∞, -9] -12
-11
-10
-9
-8
-7
-6
-11
-10
-9
-8
-7
-6
-11
-10
-9
-8
-7
-6
-11
-10
-9
-8
-7
-6
B) (-9, ∞) -12
C) [-9, ∞) -12
D) (-∞, -9) -12
3
D) positive
7)
8) 24x + 8 > 4(5x + 7)
8)
A) [5, ∞) 2
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
6
7
8
3
4
5
6
7
8
B) (5, ∞) 2
C) (-∞, 5) 2
D) (-∞, 5] 2
Use the REGRESSION feature on a graphing calculator. 9) A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Hours in lab 10 Grade (percent) 96
11 51
9)
16 9 7 15 16 10 62 58 89 81 46 51
Use linear regression to find a linear function that predicts a student's course grade as a function of the number of hours spent in lab. A) y = 0.930 + 44.3x B) y = 44.3 + 0.930x C) y = 1.86 + 88.6x D) y = 88.6 - 1.86x Use the graph to find the average rate of change. 10)
10)
y 10
5
-10
-5
5
10 x
-5
-10
A) -
1 2
B) - 2
C) 2
4
D)
1 2
Solve the problem. Express your answer as an integer or simplified fraction. 5x - 7 = 7x + 3 11) 5 2 A) - 1 25
1 45
B)
C) - 29 25
11) D)
29 45
Write the slope-intercept equation (y = mx + b) for a line with the given characteristics. 12) m = - 4, y-intercept (0, -7) A) y = - 4x B) y = - 4x - 7 C) 4x + y = - 7 D) y = - 7x - 4 Find the slope of the line containing the given points. 13) (-5, 2) and (0, 2) 5 A) B) 0 2
12)
13) C) - 5 2
D) Undefined
Provide an appropriate response. 14) Use the graph to find the slope-intercept form of the equation of the line.
14)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) y = x + 3
B) y = -x + 3
C) y = 3x
D) y = x - 3
15) Find the standard form of the equation of the line with slope of - 2 and passing through (4, 4). 7 A) 2x + 7y = 36
B) 2x + 7y = - 36
C) 2x - 7y = 36
D) 7x + 2y = - 36
Find the slope and y intercept of the graph of the equation. 3 16) y = 5 x 2 2 A) Slope =
16)
3 ; y intercept = 5 2 2
3 B) Slope = 5 ; y intercept = 2 2
3 ; y intercept = 5 2 2
3 D) Slope = 5 ; y intercept = 2 2
C) Slope = -
5
15)
Solve the problem. Express your answer as an integer or simplified fraction. 17) Solve: x - 2 - x - 3 = 3 - x - 3 3 6 2 A) 2
B) 3
C) - 3
Write an equation of the line with the indicated slope and y intercept. 18) Slope = 1; y intercept = -5 A) y = -5x - 1 B) y = x - 5 C) y = -x - 5
17) D) - 2
18) D) y = -5x + 1
Use the REGRESSION feature on a graphing calculator. 19) For some reason the quality of production decreased as the year progressed at a flash drive manufacturing plant. The following data represent the percentage of defective flash drives produced at the plant in the corresponding month of the year. Month, x % defective, y
2 1.3
3 1.6
5 2.0
7 2.4
8 2.6
19)
9 12 2.8 3.1
Use the regression equation with values rounded to four decimals to predict the percentage of defective drives in month 6, June. A) 2.15% B) 2.3% C) 2.20% D) 2.0% Write an equation of the line with the indicated slope and y intercept. 7 20) Slope = 5 ; y intercept = 2 2 A) y = -
7 x+ 5 2 2
21) Slope = 2, y intercept = -4 A) y = -2x - 4
20)
7 B) y = 5 x + 2 2
7 C) y = 5 x 2 2
D) y =
7 x- 5 2 2
B) y = 2x - 4
C) y = 4x - 2
D) y = 4x + 2
21)
Determine whether the slope of the line is positive, negative, zero, or undefined. 22)
22)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) negative
B) zero
C) positive
6
D) undefined
Write an equation of the line with the indicated slope and y intercept. 23) Slope = - 1 ; y intercept = -5 2 A) y = -5x + 1 2
B) y = x - 5 2
C) y = -5x - 1 2
23) D) y = - x - 5 2
Solve the problem. 24) The cost of manufacturing a computer part is related to the quantity produced, x, during a production run. When 100 parts are produced, the cost is $300. When 600 parts are produced, the cost is $ 4800. Find an equation of the line relating quantity produced to cost. Write the final answer in the form C = mx + b. A) C = 9x B) C = 9x - 600 C) C = 600x + 9 D) C = 9x + 600 Provide an appropriate response. 25) Given two points (x1, y 1) and (x2, y 2), the ratio of the change in y to the change in x is called. A) break-even point C) equilibrium point
Solve the problem. 27) The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge of $25 for the repairman to come to the house, to which a charge of $20 per hour is added. Find an equation that can be used to determine the labor cost, C, of a repair that takes x hours. Write the final answer in the form C = mx + b. A) C = -20x + 25 B) C = 45x C) C = 25x + 20 D) C = 20x + 25 28) Find the Celsius temperature (to the nearest degree) when Fahrenheit temperature is 50° by solving the equation 50 = 9 C + 32, where F is the Fahrenheit temperature (in degrees) and C is 5 B) 122°C
C) 10°C
B) Slope = 5; y intercept = 1 2
C) Slope = - 1 ; y intercept = -5 2
D) Slope = - 1 ; y intercept = 5 2
Solve the problem. Express your answer as an integer or simplified fraction. x -4= x -3 30) 6 3 C) - 14 7
27)
28)
29)
A) Slope = 5; y intercept = - 1 2
B) - 6
26)
D) 96°C
Find the slope and y intercept of the graph of the equation. 29) y = - x + 5 2
A) - 2
25)
B) x-intercept D) slope
Write the slope-intercept equation (y = mx + b) for a line with the given characteristics. 26) m = 3, passing through (1, -2) A) y = 3x B) y = 5x - 3 C) y = 3x - 5 D) y - 5 = 3x
the Celsius temperature. A) 24°C
24)
30) D) 14
Provide an appropriate response. 31) Find the standard form of the equation of the line passing through the two points. (2, - 6) and (- 9, 6) A) - 8x + 15y = - 18 B) 12x + 11y = - 42 C) 8x - 15y = - 18 D) - 12x + 11y = - 42
31)
Use the REGRESSION feature on a graphing calculator. 32) Efficiency experts rate employees according to job performance and attitude. The results for several randomly selected employees are given below.
32)
Attitude, x 59 63 65 69 58 77 76 69 70 64 Performance, y 72 67 78 82 75 87 92 83 87 78 Find the regression line which can be used to predict performance rating if attitude rating is known. A) y = 92.3 - 0.669x B) y = -47.3 + 2.02x C) y = 11.7 + 1.02x D) y = 2.81 + 1.35x Solve the problem. Express your answer as an integer or simplified fraction. 33) -2(2x + 5) - 4 = -2(x + 2) + 4x 5 1 A) B) C) - 5 3 6 Find the slope of the line containing the given points. 34) (6, 1) and (6, - 4) A) 0 B) - 1 4
33) D)
34) C) - 4
D) Undefined
Use the graph to find the average rate of change. 35)
35)
y 10
5
-10
-5
10 x
5
-5
-10
A) 1
5 6
B) -4
C) -1
8
D) 4
Use the REGRESSION feature on a graphing calculator. 36) The paired data below consists of the temperature on randomly chosen days and the amount of a certain kind of plant grew (in millimeters). Temp, x Growth, y
62 36
76 50 39 50
51 13
71 33
46 33
36)
51 44 79 17 6 16
Find the linear function that predicts a plant's growth as a function of the temperature. Round your answer to two decimal places. A) y = 14..57x + 0.21 C) y = - 9.19x3 + 0.11x2 - 2.90x + 6.54
B) y = 0.21x + 14.57 D) y = - 0.06 x2 + 7.20x - 191.23
Solve the formula for the specified variable. 37) Solve: D = 4 (mx - mb) for m 5 A) m =
4D 5(x + b)
B) m =
37) 5D 4(x + b)
C) m =
Find the slope and y intercept of the graph of the equation. 38) y = x + 3 A) Slope = 3; y intercept = 1 C) Slope = 0; y intercept = -3
5D 4(x - b)
4D 5(x - b)
D) m =
38) B) Slope = 3; y intercept = -1 D) Slope = 1; y intercept = 3
Solve the problem. Express your answer as an integer or simplified fraction. 39) 7x - (5x - 1) = 2 1 1 A) - 1 B) C) 2 12 2
39) D) - 1 12
Write an equation of the line with the indicated slope and y intercept. 3 26 40) Slope = - ; y intercept = 5 5 A) y = -
3 26 x+ 5 5
B) y = -
3 26 x5 5
C) y = -
40) 5 26 x+ 3 5
D) y =
3 16 x+ 5 5
Provide an appropriate response. 41) Find the line passing through the two points. Write the equation in standard form. (10, 9) and (10, 1) A) x + y = 11 B) x = 10 C) x + y = 19 D) y = 9 Find the slope of the line containing the given points. 42) (5, -3); (-8, 2) 13 13 A) B) 5 5
41)
42) 5 C) 13
9
5 D) 13
Solve the problem. 43) At a local grocery store the demand for ground beef is approximately 50 pounds per week when the price per pound is $4, but is only 40 pounds per week when the price rises to $5.50 per pound. Assuming a linear relationship between the demand x and the price per pound p, express the price as a function of demand. Use this model to predict the demand if the price rises to $5.80 per pound. A) p = 11.5x + -0.15; 40 pounds B) p = - 0.15x + 11.5; 38 pounds C) p = - 0.15x - 11.5; 40 pounds D) p = 0.15x + 11.5; 38 pounds 44) Assume that the price per unit d of a certain item to the consumer is given by the equation d = 35 - .10x, where x is the number of units in demand. The price per unit from the supplier is given by the equation s = .2x + 20, where x is the number of units supplied. Find the equilibrium price and the equilibrium quantity. A) equilibrium price: $30 per unit; equilibrium quantity: 50 units B) equilibrium price: $20 per unit; equilibrium quantity: 50 units C) equilibrium price: $50 per unit; equilibrium quantity: 30 units D) equilibrium price: $35 per unit; equilibrium quantity: 50 units Graph the linear equation and determine its slope, if it exists. 45) 3x + 5y = 11 y
8 6 4 2 2
4
6
8 10
x
-4 -6 -8 -10
A) slope: 3 4
B) slope: - 3 4 y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2 -2
2
4
6
8 10
x
-10 -8 -6 -4 -2 -2
-4
-4
-6
-6
-8
-8
-10
-10
10
44)
45)
10
-10 -8 -6 -4 -2 -2
43)
2
4
6
8 10
x
C) slope: 3 4
D) slope: - 3 4 y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2 -2
2
4
6
8 10
x
-10 -8 -6 -4 -2 -2
-4
-4
-6
-6
-8
-8
-10
-10
2
4
6
8 10
x
Solve the problem. Express your answer as an integer or simplified fraction. x - 5 = x+6 46) 16 8 8 A) - 16
B) - 17
C) - 22
Solve the formula for the specified variable. 47) 7x + 10y = 19 for y A) y = - 7 x + 19 10 10
46) D) - 11
47) B) - 7x - 10y = -19
C) y = 7 x + 19 10 10
D) y = 7x - 19
Use the REGRESSION feature on a graphing calculator. 48) The use of bottled water in the United States has shown a steady increase in recent years. The table shows the annual per capita consumption for the years 1995 - 2001. Year 1995 1996 1997 1998 1999 2000 2001 Gallons/person 4.4 5.1 5.7 6.4 7.3 8.0 10.2 With x being the years since 1995, find the linear function that represents this data. Round your answer to two decimal places. A) y = 0.1x2 + 0.29x + 4.57 B) y = 4.07x + 0.89 D) y = 0.04x3 - 0.23x2 + 1.01x + 4.35
C) y = 0.89x + 4.07
11
48)
Provide an appropriate response. 49) Write the equation of the line in the following graph.
49)
y 3 2 1 -6 -5 -4 -3 -2 -1 -1
1 2 3 4 5 6x
-2 -3
A) f(x) = 1 x - 1 3
B) f(x) = 1 x + 1 3
C) f(x) = - 1 x + 1 3
D) f(x) = - 1 x - 1 3
Solve the formula for the specified variable. 50) F = 9 C + 32 for C 5 A) C = 9 (F - 32) 5
B) C =
50) 5 F - 32
C) C = 5 (F - 32) 9
D) C = F - 32 9
Determine whether the slope of the line is positive, negative, zero, or undefined. 51)
51)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) zero
B) undefined
C) positive
Provide an appropriate response.
12
D) negative
52) Graph the linear function defined by f(x) = 2 x + 2 and indicate the slope and intercepts. 3 5 4 3 2 1 -5 -4 -3 -2 -1 -1
y
1 2 3 4 5 x
-2 -3 -4 -5
A) x-intercept = -2; y-intercept = 3; slope 2 3 5 4 3 2 1
y
1 2 3 4 5 x
-5 -4 -3 -2 -1 -1 -2 -3 -4 -5
B) x-intercept = 3; y-intercept = -2; slope 2 3 5 4 3 2 1 -5 -4 -3 -2 -1 -1
y
1 2 3 4 5 x
-2 -3 -4 -5
13
52)
C) x-intercept = -3; y-intercept = 2; slope 2 3 5 4 3 2 1
y
1 2 3 4 5 x
-5 -4 -3 -2 -1 -1 -2 -3 -4 -5
D) x-intercept = 2; y-intercept = -3; slope 2 3 5 4 3 2 1 -5 -4 -3 -2 -1 -1
y
1 2 3 4 5 x
-2 -3 -4 -5
14
Graph the equation. 53) 42 + 6y = 0
53) y
10 5
-10
-5
10 x
5 -5 -10
A)
B) 10
y
10
5
-10
y
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D) 10
y
10
5
-10
-5
y
5
5
10 x
-10
-5
-5
-5
-10
-10
Solve the problem. 54) Suppose the sales of a particular brand of MP3 player satisfy the relationship S = 200x + 3800 , where S represents the number of sales in year x, with x = 0 corresponding to 2002 . Find the number of sales in 2005. A) 4200 B) 12,600 C) 6400 D) 4400 Provide an appropriate response. 55) Find the line passing through the two points. Write the equation in standard form. (-3, 6) and (6, 6) A) -2x - y 0 B) -x - 2y = 0 C) x = -2 D) y = 6
15
54)
55)
Determine whether the slope of the line is positive, negative, zero, or undefined. 56)
56)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) negative
B) positive
C) zero
D) undefined
Find the slope and y intercept of the graph of the equation. 4 18 57) y = - x + 5 5 A) Slope =
57)
4 8 ; y intercept = 5 5
B) Slope =
5 8 ; y intercept = 4 5
4 18 ; y intercept = 5 5
D) Slope =
4 18 ; y intercept = 5 5
C) Slope = -
Solve the problem. 58) A piece of equipment was purchased by a company for $10,000 and is assumed to have a salvage value of $3,000 in 10 years. If its value is depreciated linearly from $10,000 to $3,000, find a linear equation in the form V = mt + b, t time in years, that will give the salvage value at any time t, 0 ≤ t ≤ 10. A) T = - 700V + 10,000 B) V = - 700t - 10,000 C) V = - 700t + 10,000 D) V = 700t + 10,000 Solve the problem. Express your answer as an integer or simplified fraction. 1 1 59) - (x - 18 ) - (x - 8 ) = x - 7 6 8 A)
120 31
B)
264 31
C)
16
216 31
58)
59) D)
72 31
Provide an appropriate response. 60) Use the graph to find the slope, x-intercept and y-intercept of the line.
60)
y 10 8 6 4 2 -10 -8 -6 -4 -2 -2
2
4
6
8
10 x
-4 -6 -8 -10
A) slope = -1 x-intercept = (7, 0) y-intercept = (0, -7) C) slope = 1 x-intercept = (0, 7) y-intercept = (-7, 0)
B) slope = 1 x-intercept = (7, 0) y-intercept = (0, -7) D) slope = - 1 x-intercept = (-7, 0) y-intercept = (0, 7)
Solve the inequality and graph. Express your answer in interval notation. 61) -4(-2 - x) < 6x + 19 - 11 - 2x
A) (-∞, 8)
0
61)
B) ∅
1
2
3
4
5
6
7
8
-5 -4 -3 -2 -1
9
C) (-∞, 0)
-5 -4 -3 -2 -1
0
1
2
3
4
0
1
2
3
4
D) (-∞, ∞)
0
1
2
3
-5 -4 -3 -2 -1
4
Solve the problem. 62) The mathematical model C = 600 x + 30,000 represents the cost in dollars a company has in manufacturing x items during a month. Using this model, how much does it cost to produce 600 items? A) $0.08 B) $390,000 C) $360,000 D) $50.00 Find the slope and y intercept of the graph of the equation. 63) y = -4x + 6 A) Slope = 6, y intercept = -4 C) Slope = -6, y intercept = -4 17
62)
63) B) Slope = 4, y intercept = -6 D) Slope = -4, y intercept = 6
Use the REGRESSION feature on a graphing calculator. 64) In the table below, x represents the number of years since 2000 and y represents sales (in thousands of dollars) of a clothing company. Use the regression equation to estimate sales in the year 2006. Round to the nearest thousand dollars.
64)
Year x 1 2 3 4 5 Sales y 84 76 39 30 26 A) $20,000
B) $2,000
C) $14,000
D) $8,000
Solve the problem. 65) A small company that makes hand-sewn leather shoes has fixed costs of $320 a day, and total costs of $1200 per day at an output of 20 pairs of shoes per day. Assume that total cost C is linearly related to output x. Find an equation of the line relating output to cost. Write the final answer in the form C = mx + b. A) C = 60x + 320 B) C = 44x + 1520 C) C = 44x + 320 D) C = 60x + 1520 66) You have $50,000 and wish to invest part at 10% and the rest at 6%. How much should be invested at each rate to produce the same return as if it all had been invested at 9%? A) $37,000 at 10%, $13,000 at 6% B) $37,500 at 10%, $12,500 at 6% C) $37,500 at 6%, $12,500 at 10% D) $37,000 at 6%, $13,000 at 10% Solve the formula for the specified variable. 67) S = 2!rh + 2!r2 for h A) h = S - 2!r 2!r
2
65)
66)
67)
B) h = S - r
C) h = 2!(S - r)
D) h = S - 1 2!r
Provide an appropriate response. 68) Write the equation of a line that passes through (3, 9) and (0, -7). Write the final answer in the form Ax + By = C where A, B, and C are integers with no common divisors (other than ±1) and A > 0. A) 3x - 16y = 21 B) -16x + 3y = 21 C) 16x - 3y = -21 D) 16x - 3y = 21 Write an equation of the line with the indicated slope and y intercept. 69) Slope = -3, y intercept = 5 A) y = -3x - 5 B) y = 5x - 3 C) y = -3x + 5
69) D) y = 3x + 5
Solve the problem. 70) Using a phone card to make a long distance call costs a flat fee of $0.85 plus per $0.19 minute starting with the first minute. Find the total cost of a phone call which lasts 8 minutes. A) $6.00 B) $2.37 C) $1.52 D) $8.16 Find the slope and y intercept of the graph of the equation. 71) y = 2x - 6 A) Slope = 2, y intercept = -6 C) Slope = 2, y intercept = 6
18
68)
70)
71) B) Slope = 6, y intercept = 2 D) Slope = -6, y intercept = 2
Answer Key Testname: CHAP 01_14E
1) B 2) A 3) B 4) D 5) C 6) C 7) D 8) B 9) D 10) A 11) C 12) B 13) B 14) B 15) A 16) D 17) D 18) B 19) A 20) C 21) B 22) D 23) D 24) B 25) D 26) C 27) D 28) C 29) D 30) B 31) B 32) C 33) A 34) D 35) A 36) B 37) C 38) D 39) B 40) A 41) B 42) C 43) B 44) A 45) B 46) C 47) A 48) C 49) D 19
Answer Key Testname: CHAP 01_14E
50) C 51) A 52) C 53) D 54) D 55) D 56) B 57) C 58) C 59) B 60) B 61) B 62) B 63) D 64) B 65) C 66) B 67) A 68) D 69) C 70) B 71) A
20
CHAPTER 2
Exam Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) For f(t) = 3t + 2 and g(t) = 2 - t2, find 4f(3) - g(-3) + g(0).
1)
2) The following graph represents the result of applying a sequence of transformations to the graph of a basic function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.
2)
y 9 8 7 6 5 4 3 2 1 -5 -4 -3 -2 -1
1 2 3 4 5 x
3) For f(t) = 3 - 5t, find f(a + h) - f(a) . h
3)
4) Find the vertex and the maximum or minimum of the quadratic function f(x) = -x2 - 4x + 5 by first writing f in standard form. State the range of f and find the
4)
intercepts of f . 5) If f(x) =
x- 3 x2
if x < 2
, what is the definition of g(x), the function whose graph is if x ≥ 2 obtained by shifting f(x)'s graph right 5 units and down 1 unit?
Solve the problem. 6) In the table below, the amount of the U.S. minimum wage is listed for selected years. U.S. Minimum Wage Year 1961 1967 1974 1980 1981 1990 1991 1996 1997 Wage $1.15 $1.40 $2.00 $3.10 $3.35 $3.80 $4.25 $4.75 $5.15 Find an exponential regression model of the form y = a ∙ b x, where y represents the U.S. minimum wage x years after 1960. Round a and b to four decimal places. According to this model, what will the minimum wage be in 2005? In 2010?
1
5)
6)
7) The financial department of a company that produces digital cameras arrived at the following price -demand function and the corresponding revenue function:
7)
p(x) = 95.4 - 6x price-demand R(x) = x ∙ p(x) = x(95.4 - 6x) revenue function The function p(x) is the wholesale price per camera at which x million cameras can be sold and R(x) is the corresponding revenue (in million dollars). Both functions have domain 1 ≤ x ≤ 15. They also found the cost function to be C(x) = 150 + 15.1x (in million dollars) for manufacturing and selling x cameras. Find the profit function and determine the approximate number of cameras, rounded to the nearest hundredths, that should be sold for maximum profit. Provide an appropriate response. 8) Graph f(x) = -x2 - x + 6 and indicate the maximum or minimum value of f(x), whichever
8)
exists. 8
y
6 4 2 -8 -6 -4 -2 -2
2
4
6
8x
-4 -6 -8
Use the REGRESSION feature on a graphing calculator. 9) A particular bacterium is found to have a doubling time of 20 minutes. If a laboratory culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how many bacteria will be present in 55 minutes? Use six decimal places in the interim calculation for the growth rate. Solve the problem. 10) The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: C(x) = 1500 + 105x + x2. The average cost per unit at a production level of players per day is C(x) = C(x) . x (A) Find the rational function C. (B) Graph the average cost function on a graphing utility for 10 ≤ x ≤ 200. (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)?
2
9)
10)
Provide an appropriate response. 3 11) If g(x) = -4x2 + x - 9, find g(-2), g(1), and g . 2
11)
12) The following graph represents the result of applying a sequence of transformations to the graph of a basic function. Identify the basic function and describe the transformation(s). Write the equation for the given graph. 2 1 -14-12-10 -8 -6 -4 -2 -1
12)
y
2 4 6 x
-2 -3 -4 -5 -6 -7 -8 -9 -10
13) Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of the following correspondences define a function. Explain. (A) A student corresponds to the teacher if the student is enrolled in the teacher's class. (B) A student corresponds to every teacher of the school.
13)
14) Only one of the following functions has domain which is not equal to all real numbers. State which function and state its domain. (A) h(x) = 4x2 - 3x - 5 (B) f(x) = 2x (C) g(x) = x + 7 48 - x 2
14)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert to a logarithmic equation. 15) e t = 7 A) log 7 e = t
15) B) log 7 t = e
C) ln 7 = t
D) ln t = 7
Find the function value. 2 16) f(x) = x + 8 ; f(5) x3 - 2x A)
33 125
16) B)
5 23
C)
3
33 115
D)
11 41
Write an equation for the graph in the form y = a(x - h)2 + k, where a is either 1 or -1 and h and k are integers. 17) 17) 10
y
5
-10
-5
5
10 x
-5 -10
A) y = -(x - 3 ) 2 - 2
B) y = -(x + 3 ) 2 + 2
C) y = (x + 3 ) 2 + 2
D) y = (x + 3 ) 2 -
1 3
Provide an appropriate response. 18) What is the minimum number of x intercepts that a polynomial of degree 11 can have? Explain. A) 0 because a polynomial of odd degree may not cross the x axis at all. B) 11 because this is the degree of the polynomial. C) 1 because a polynomial of odd degree crosses the x axis at least once. D) Not enough information is given. Solve the problem. 19) To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. W is a linear function of h. Find the ideal minimum weight of a woman whose height is 62 inches. A) 118 lb B) 378 lb C) 130 lb D) 120 lb
4
18)
19)
Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 20) f(x) = x2 + 4x + 3 A) Standard form: f(x) = (x + 2) 2 - 1
20)
B) Standard form: f(x) = (x - 2) 2 - 1
(A) x-intercepts: - 3 , -1; y-intercept: 3 (B) Vertex (2, -1) (C) Minimum: -1 (D) y ≥ -1
(A) x-intercepts: 1, 3; y-intercept: 3 (B) Vertex (-2, -1) (C) Minimum: -1 (D) y ≥ -1
C) Standard form: f(x) = (x + 2) 2 - 1 (A) x-intercepts: - 3 , -1; y-intercept: 3 (B) Vertex (-2, -1) (C) Minimum: -1 (D) y ≥ -1
D) Standard form: f(x) = (x - 2) 2 - 1 (A) x-intercepts: - 3 , -1; y-intercept: 3 (B) Vertex (-2, -1) (C) Maximum: -1 (D) y ≤ -1
Give the domain and range of the function. 21) r(x) = x - 3 - 5 A) Domain: all real numbers; Range: all real numbers B) Domain: [- 5 , ∞); Range: all real numbers C) Domain: all real numbers; Range: [0, ∞) D) Domain: all real numbers; Range: [- 5 , ∞)
21)
Provide an appropriate response. 22) What is the maximum number of x intercepts that a polynomial of degree 10 can have? A) 9 B) 11 C) 10 D) Not enough information is given. Use a calculator to evaluate the expression. Round the result to five decimal places. 23) log (-10.25) A) -1.01072 B) 2.32728 C) 1.01072 Graph the function. 24) f(x) = 5 x
23) D) Undefined
24) y
4 2
-4
22)
-2
2
4
x
-2 -4
5
A)
B) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
C)
2
4
x
2
4
x
D) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
Solve the problem. 25) In North America, coyotes are one of the few species with an expanding range. The future population of coyotes in a region of Mississippi valley can be modeled by the equation P = 59 + 12 ∙ ln(18t + 1) , where t is time in years. Use the equation to determine when the population will reach 170. (Round your answer to the nearest tenth year.) A) 581.3 years B) 578.0 years C) 583.1 years D) 586.2 years 26) The function P, given by P(d) = 1 d + 1, gives the pressure, in atmospheres (atm), at a depth d, in 33
25)
26)
feet, under the sea. Find the pressure at 200 feet. Round your answer to the nearest whole number. A) 200 atm B) 8 atm C) 201 atm D) 7 atm Determine whether the function is linear, constant, or neither 27) y = x + 3 7 A) Linear
B) Constant
27) C) Neither
6
Solve graphically to two decimal places using a graphing calculator. 28) 1.7x2 - 2.6 x - 3.9 > 0 A) x < -0.93 or x > 2.46 C) -2.46 < x < 0.93
28)
B) -0.93 < x < 2.46 D) x < -2.46 or x > 0.93
Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. 29) 29) y 10 5
-10
-5
5
10
x
-5 -10
A) f(x) = x2 + 6 x + 5 C) f(x) = x2 - 6 x + 5
B) f(x) = x2 + 5 x + 6 D) f(x) = x2 + 5 x - 6
Use the REGRESSION feature on a graphing calculator. 30) Since 1984 funeral directors have been regulated by the Federal Trade Commission. The average cost of a funeral for an adult in a Midwest city has increased, as shown in the following table.
YEAR 1980 1985 1991 1995 1996 1998 2001
AVERAGE COST OF FUNERAL $ 1926 $ 2841 $ 3842 $ 4713 $ 4830 $ 5120 $ 5340
Let x represent the number of years since 1980. Use a graphing calculator to fit a quartic function to the data. Round your answer to five decimal places. A) y = 170.5971x + 1991.5213 B) y = -0.04268 x4 + 1.53645x3 - 16.76289x2 + 231.82723x + 1927.58518 C) y = -0.04268 x4 D) y = -2.047489 x2 + 212.82699x + 1879.85469
7
30)
Give the domain and range of the function. 31) h(x) = -2 x A) Domain: [0, ∞); Range: [0, ∞) B) Domain: all real numbers; Range: (-∞, 0] C) Domain: (-∞, 0]; Range: all real numbers D) Domain: all real numbers; Range: (-∞, 4]
31)
Find the x-intercept(s) if they exist. 32) 6x2 = 42x A) 7
32) B) 0, 7
C) 0
D) 21
Determine whether the function is linear, constant, or neither 33) y = 2 ! 3 A) Linear
B) Constant
33) C) Neither
8
Graph the function using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. 34) f(x) = 4 - ln x 34) y 5
-5
x
5
-5
A) Decreasing: (0, ∞)
B) Increasing (4, ∞) y
y
5
5
-5
5
x
-5
-5
5
x
5
x
-5
C) Decreasing: (0, ∞)
D) Increasing (0, ∞) y
y
5
5
-5
5
x
-5
-5
-5
Solve the equation. 35) Solve for x: 3 (1 + 2x) = 27 A) -1
35) B) 3
C) 9
D) 1
Solve the problem. 36) The U. S. Census Bureau compiles data on population. The population (in thousands) of a southern city can be approximated by P(x) = 0.08x2 - 13.08x + 927, where x corresponds to the years after 1950. In what calendar year was the population about 804,200? A) 2000 B) 1955 C) 1965
9
D) 1960
36)
37) The polynomial 0.0053x3 + 0.003x2 + 0.108x + 1.54 gives the approximate total earnings of a company, in millions of dollars, where x represents the number of years since 1996. This model is valid for the years from 1996 to 2000. Determine the earnings for 2000. Round to 2 decimal places. A) $2.03 million B) $2.36 million C) $2.82 million D) $2.26 million For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 38) m(x) = -(x + 3 ) 2 + 4
37)
38)
A) (A) x-intercepts: - 5 , -1; y-intercept: -5 (B) Vertex (-3, 4) (C) Maximum: 4 (D) y ≤ 4 B) (A) x-intercepts: - 5 , -1; y-intercept: -5 (B) Vertex (-3, 4) (C) Minimum: 4 (D) y ≥ 4 C) (A) x-intercepts: - 5 , -1; y-intercept: -5 (B) Vertex (3, -4) (C) Maximum: 4 (D) y ≤ 4 D) (A) x-intercepts: 1, 5; y-intercept: -5 (B) Vertex (-3, 4) (C) Maximum: 4 (D) y ≤ 4
Solve the equation. 39) Solve for x: 24x = 8 x + 5 A) -15
39) B) 5
C) 15
D) -5
Solve the problem. 40) A country has a population growth rate of 2.4% compounded continuously. At this rate, how long will it take for the population of the country to double? Round your answer to the nearest tenth. A) 30 years B) 28.9 years C) 2.9 years D) .29 years
10
40)
Use the REGRESSION feature on a graphing calculator. 41) A strain of E-coli Beu-recA441 is placed into a petri dish at 30 ∘Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured.
41)
Time in hours , x Population, y 0 0.09 2.5 0.18 3.5 0.26 4.5 0.35 6 0.50 Find the exponential equation in the form y = a ∙ b x, where x is the hours of growth. Round to four decimal places. A) y = 1.3384 x B) y = 0.0903 x C) y = 1.3384 ∙ 0.0903 x Write in terms of simpler forms. 42) logb M9 A) 9 + logb M
D) y = 0.0903 ∙ 1.3384 x
42) B) M logb 9
C) M + logb 9
D) 9 logb M
Use point-by-point plotting to sketch the graph of the equation. 43) f(x) = 2x x- 4
43)
y
10 5
-10
-5
10 x
5 -5 -10
A)
B) 10
y
10
5
-10
-5
y
5
5
10 x
-10
-5
5
-5
-5
-10
-10
11
10 x
C)
D) 10
y
10
5
-10
y
5
-5
5
10 x
-10
-5
5
-5
-5
-10
-10
10 x
The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? 44) 44) y
10
6 x
-6 -10 -20
A) (i) 3 (ii) Positive
B) (i) 4 (ii) Negative
C) (i) 3 (ii) Negative
Provide an appropriate response. 45) In a profit-loss analysis, point where revenue equals cost. A) profit-loss point B) turning point C) break-even point D) inflection point Determine the domain of the function. 46) f(x) = - 7x + 9
D) (i) 4 (ii) Positive
45)
46)
A) All real numbers except 9 7
B) x ≤ 9 7
C) No solution
D) All real numbers
For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x).
12
47) f(x) = -2x - 3 x+2
47) 8
y
4
-8
-4
8 x
4 -4 -8
A) (i) x intercept: - 3 ; y intercept: - 3 2 2 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -2 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
B) (i) x intercept: 3 ; y intercept: - 3 2 2 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -2 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
13
C) (i) x intercept: - 3 ; y intercept: - 3 2 2 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -2 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
D) (i) x intercept: 3 ; y intercept: - 3 2 2 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -2 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. 48) x2 + y 2 = 36 48) A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6 Determine the domain of the function. 49) f(x) = 3 - x A) x < 3 C) No solution
49) B) All real numbers except 3 D) x ≤ 3
14
Graph the function using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. 50) f(x) = 2 - ln(x + 4) 50) y
10 5
-10
-5
10 x
5 -5 -10
A) Decreasing: (-4, ∞) 10
B) Decreasing: (-4, ∞)
y
10
5
-10
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C) Decreasing: (0, ∞) 10
-5
5
10 x
5
10 x
D) Decreasing: (4, ∞) y
10
5
-10
y
y
5
5
10 x
-10
-5
-5
-5
-10
-10
For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. 51) y = 35 - x2 + 2x 51) A) (i) 2 (ii) 7, 5 (iii) 35
B) (i) 2 (ii) 7, -5 (iii) 35
C) (i) 2 (ii) 5, -7 (iii) -35
Use a calculator to evaluate the expression. Round the result to five decimal places. 52) log 51.237 A) 51.237 B) 1.70958 C) 3.93646
15
D) (i) 2 (ii) -5, -7 (iii) -35
52) D) Undefined
For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). 53) f(x) = 3x 53) x- 2 8
y
4
-8
-4
8 x
4 -4 -8
A) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = 3 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
B) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = 3 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
16
C) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -3 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
D) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -3 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
Find the equations of any vertical asymptotes. 54) f(x) = 4x - 11 x2 + 3x - 18 A) x = 3, x = -6
54)
B) y = 4
C) y = 3, y = -6
Determine the domain of the function. 55) f(x) = 8 x3
D) x = -3, x = 6
55)
A) All real numbers except 0 C) All real numbers
B) No solution D) x < 0
17
Determine whether the graph is the graph of a function. 56)
56)
y
10 5
-10
-5
10 x
5 -5 -10
A) function
B) not a function
Graph the function. 57) f(x) = 0.9 x
57) y
4 2
-4
-2
2
4
x
-2 -4
A)
B) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
2
-2
-2
-4
-4
18
4
x
C)
D) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
2
-2
-2
-4
-4
4
x
Solve the problem. 58) If the average cost per unit C(x) to produce x units of plywood is given by C(x) = 1200 , what is x + 40 the unit cost for 10 units? A) $80.00
B) $120.00
C) $24.00
D) $3.00
59) A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= 48T2. What is his hang time? Round to the nearest tenth. A) 0.8 sec
B) 0.6 sec
C) 1 sec
60)
D) A = 2200 (1.03) 2t
61) If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact. [A = P(1 + r)t] A) 6 years
59)
D) 0.9 sec
60) Suppose that $2200 is invested at 3% interest, compounded semiannually. Find the function for the amount of money after t years. A) A = 2200 (1.015) t B) A = 2200 (1.015) 2t C) A = 2200 (1.0125) 2t
58)
B) 5 years
C) 2 years
19
D) 8 years
61)
The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? 62) 62) y
6x
-6
A) (i) 4 (ii) Negative
B) (i) 3 (ii) Negative
C) (i) 3 (ii) Positive
D) (i) 4 (ii) Positive
Solve the equation graphically to four decimal places. 63) Let f(x) = -0.6 x2 + 3x + 1, find f(x) = 5.
63)
A) 2.5000 C) No solution
B) 4.7500 D) 2.5000 , 4.7500
Determine whether the relation represents a function. If it is a function, state the domain and range. 64) Bob Ann Dave
64)
carrots peas squash
A) function domain: {carrots, peas, squash} range: {Bob, Ann, Dave} B) function domain: {Bob, Ann, Dave} range: {carrots, peas, squash} C) not a function Find the function value. 65) Find f(4) when f(x) = 9 - 8x2. A) -119 B) -23
65) C) 137
D) -55
Solve the equation. 66) Solve for t: e -0.07t = 0.05 A) -66.4815
Round your answer to four decimal places. B) 42.7962 C) 44.321
20
66) D) -70.1312
Find the equation of any horizontal asymptote. 2 67) f(x) = 7x - 2x - 4 4x2 - 5 x + 6 A) y =
2 5
B) y =
67)
7 4
C) y = 0
D) None
Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. 68) x - y 2 = 9 68) A) A function with domain ℛ B) Not a function; for example, when x = 10, y = ±1 Solve the problem. 69) A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays according to the equation A = A0 e -0.000124t). A) 15,035 years B) 1,500 years C) 15, 000 years D) 150 years 70) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x) represents the total profit for producing x widgets. Given R(x) = 60x - 0.4 x2 and C(x) = 3x + 13, find P(100). A) 313
B) 2000
C) 1687
71)
72) y 4 2
-4
70)
D) 55687
71) U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) = 51.42 + 15.473 ∙ log x , where x = 0 is 1980. How many families were there in 2002? A) 21 million B) 48 million C) 90 million D) 72 million Graph the function. 1 x 72) f(x) = 5
69)
-2
2
4
x
-2 -4
21
A)
B) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
C)
2
4
x
2
4
x
D) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. 73) y = x2 - 100 73) A) (i) 2 (ii) -10, 10 (iii) -100
B) (i) 1 (ii) 50 (iii) -100
C) (i) 1 (ii) 10 (iii) -100
Graph by converting to exponential form first. 74) y = log (x - 1) 2
74)
y 4 2 -4
-2
2
4
D) (i) 2 (ii) -11, 11 (iii) -100
x
-2 -4
22
A)
B) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
C)
2
4
x
2
4
x
D) y
-4
y
4
4
2
2
-2
2
4
x
-4
-2
-2
-2
-4
-4
Solve the problem. 75) If $1250 is invested at a rate of 8 1 % compounded monthly, what is the balance after 10 years? 4 [A = P(1 + i)n] A) $2281.25
B) $1594.31
C) $1031.25
D) $2844.31
Find the equations of any vertical asymptotes. 2 76) f(x) = x - 100 (x - 3 )(x + 7) A) x = 10, x = -10
75)
76)
B) y = 3, y = -7
C) x = -3
23
D) x = 3, x = -7
For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 77) n(x) = -(x - 3 ) 2 + 4
77)
A) (A) x-intercepts: -5, - 1; y-intercept: -5 (B) Vertex (3, 4) (C) Maximum: 4 (D) y ≤ 4 B) (A) x-intercepts: 1, 5; y-intercept: -5 (B) Vertex (3, 4) (C) Minimum: 4 (D) y ≥ 4 C) (A) x-intercepts: 1, 5; y-intercept: -5 (B) Vertex (-3, -4) (C) Maximum: 4 (D) y ≤ 4 D) (A) x-intercepts: 1, 5; y-intercept: -5 (B) Vertex (3, 4) (C) Maximum: 4 (D) y ≤ 4
Write in terms of simpler forms. a log4 b 78) 4 A) ab
78) B) b a
C) a4b
D) b 4a
Find the equations of any vertical asymptotes. 79) f(x) = x - 1 x2 + 2 A) x = 2
79)
B) x = -2
C) x = 1, x = -1
D) None
Solve the problem. 80) A sample of 800 grams of radioactive substance decays according to the function A(t) = 800e -0.028t, where t is the time in years. How much of the substance will be left in the sample after 10 years? Round to the nearest whole gram. A) 800 grams B) 9 grams C) 605 grams
24
D) 1 gram
80)
For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 81) f(x) = (x + 4) 2 - 9
81)
A) (A) x-intercepts: - 7, -1; y-intercept: 7 (B) Vertex (4, -9) (C) Minimum: -9 (D) y ≥ -9
B) (A) x-intercepts: - 7, -1; y-intercept: 7 (B) Vertex (-4, -9) (C) Minimum: -9 (D) y ≥ -9
C) (A) x-intercepts: 1, 7; y-intercept: 7 (B) Vertex (-4, -9) (C) Minimum: -9 (D) y ≥ -9
D) (A) x-intercepts: - 7, -1; y-intercept: 7 (B) Vertex (-4, -9) (C) Maximum: -9 (D) y ≤ -9
Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 82) n(x) = -x2 + 8 x - 7 A) Standard form: n(x) = -(x - 4) 2 + 9
82)
B) Standard form: n(x) = -(x - 4) 2 + 9
(A) x-intercepts: 1, 7; y-intercept: -7 (B) Vertex (-4, -9) (C) Maximum: 9 (D) y ≤ 9
(A) x-intercepts: 1, 7; y-intercept: -7 (B) Vertex (4, 9) (C) Maximum: 9 (D) y ≤ 9
C) Standard form: n(x) = -(x + 4) 2 + 9 (A) x-intercepts: -7, - 1; y-intercept: -7 (B) Vertex (4, 9) (C) Maximum: 9 (D) y ≤ 9
D) Standard form: n(x) = -(x + 4) 2 + 9 (A) x-intercepts: 1, 7; y-intercept: -7 (B) Vertex (4, 9) (C) Minimum: 9 (D) y ≥ 9
Solve the problem. 83) To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h. A) W(h) = 130 B) W(h) = 4h - 130 C) W(h) = 130h + 4 D) W(h) = 4 (h + 130)
25
83)
For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range 84) g(x) = (x - 1) 2 - 9
84)
A) (A) x-intercepts: - 2, 4; y-intercept: -8 (B) Vertex (1, -9) (C) Maximum: -9 (D) y ≤ -9
B) (A) x-intercepts: - 2, 4; y-intercept: -8 (B) Vertex (1, -9) (C) Minimum: -9 (D) y ≥ -9
C) (A) x-intercepts: - 2, 4; y-intercept: -8 (B) Vertex (-1, -9) (C) Minimum: -9 (D) y ≥ -9
D) (A) x-intercepts: -4, 2; y-intercept: -8 (B) Vertex (1, -9) (C) Minimum: -9 (D) y ≥ -9
Provide an appropriate response. 85) What is the minimum number of x intercepts that a polynomial of degree 8 can have? Explain. A) 1 because a polynomial of even degree crosses the x axis at least once. B) 8 because this is the degree of the polynomial. C) 0 because a polynomial of even degree may not cross the x axis at all. D) Not enough information is given. The graph of a function f is given. Use the graph to answer the question. 86) Use the graph of f given below to find f(10).
85)
86)
25
25
-25
-25 A) 15
B) -20
C) 0
Use a calculator to evaluate the expression. Round the result to five decimal places. 87) log 0.17 A) -1.76955 B) -4.07454 C) -0.76955
26
D) 10
87) D) -1.77196
Convert to a logarithmic equation. 88) 23 = 8 A) log 2 = 3 8
88) B) log 8 = 3 2
C) log2 3 = 8
D) log 8 = 2 3
Provide an appropriate response. 89) How can the graph of f(x) = - x + 1 be obtained from the graph of y = x? A) Shift it horizontally 1 units to the left. Reflect it across the x-axis. B) Shift it horizontally 1 units to the right. Reflect it across the x-axis. C) Shift it horizontally -1 units to the left. Reflect it across the x-axis. D) Shift it horizontally 1 units to the left. Reflect it across the y-axis. Use a calculator to evaluate the expression. Round the result to five decimal places. 90) log 0.234 A) 0.234 B) 1.26364 C) -1.45243
89)
90) D) -0.63074
Solve the problem. 91) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x) represents the total profit for producing x widgets. Given R(x) = 60x - 0.4 x2 and C(x) = 3x + 13, find the equation for P(x). A) P(x) = 60x - 0.4 x2 C) P(x) = -0.4 x2 + 57x - 13
91)
B) P(x) = -0.4 x2 + 63x + 13 D) P(x) = 3x + 13
Find the function value. 92) Given that f(x) = 5 x2 - 2x, find f(t + 2). A) 5t2 - 18t + 16 B) 5t2 + 18t + 16
92) C) 3t + 6
D) t2 + 2t - 6
Determine whether the graph is the graph of a function. 93) 10
93)
y
5
-10
-5
5
10 x
-5 -10
A) function
B) not a function
Use the properties of logarithms to solve. 94) log (x + 3) + log x = log 54 b b b A) 6 B) -6, -3
94) C) -6
27
D) 3
Solve for x to two decimal places (using a calculator). 95) 700 = 500 (1.04) x A) 8.58
95)
B) 520
C) 1.35
D) 1.40
For the rational function below (i) Find any intercepts for the graph; (ii) Find any vertical and horizontal asymptotes for the graph; (iii) Sketch any asymptotes as dashed lines. Then sketch a graph of f. 96) y = 18 96) x2 - 9 y 8 6 4 2 -8 -6 -4 -2 -2
2
4
6
x
8
-4 -6 -8
A) (i) y intercept: 6 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 6 and x = -6 (iii) y 8 6 4 2 -8 -6 -4 -2 -2
2
4
6
8
x
-4 -6 -8
B) (i) y intercept: - 2 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 3 and x = -3 (iii) y 8 6 4 2 -8 -6 -4 -2 -2
2
4
6
8
x
-4 -6 -8
28
C) (i) y intercept: - 2 (ii) horizontal asymptote: y = 0 (iii) y 8 6 4 2 -8 -6 -4 -2 -2
2
4
6
8
x
-4 -6 -8
D) (i) y intercept: -6 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 6 and x = -6 (iii) y 8 6 4 2 -8 -6 -4 -2 -2
2
4
6
8
x
-4 -6 -8
Solve the problem. 97) The average weight of a particular species of frog is given by w(x) = 98 x3 , 0.1 ≤ x ≤ 0.3, where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be obtained from one of the six basic functions: y = x, y = x2, y = x3 , y = x, y =
3
x, or y = x . (ii) Sketch a graph of function w using part (i) as an aid.
y
x
29
97)
A) (i) The graph of the basic function y = x3 is vertically expanded by a factor of 98. (ii) y 3
2
1
0.1
0.2
0.3
x
B) (i) The graph of the basic function y = vertically expanded by a factor of 98. (ii)
3
x is
y 75
50
25
0.1
0.2
0.3
x
C) (i) The graph of the basic function y = x2 is vertically expanded by a factor of 98. (ii) y 8 6 4 2
0.1
0.2
0.3
x
30
D) (i) The graph of the basic function y = x3 is reflected on the x-axis and is vertically expanded by a factor of 98. (ii) 2
y
0.1
0.2
0.3
x
-2
-4
For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). 98) f(x) = x - 3 98) x- 4 8
y
4
-8
-4
8 x
4 -4 -8
A) (i) x intercept: -5; y intercept: 3 4 (ii) Domain: all real numbers except -4 (iii) Vertical asymptote: x = -4; horizontal asymptote: y = 1 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
31
B) (i) x intercept: -3; y intercept: 3 4 (ii) Domain: all real numbers except -4 (iii) Vertical asymptote: x = -4; horizontal asymptote: y = 1 (iv) 8
y
4
-8
-4
8 x
4 -4 -8
C) (i) x intercept: 5; y intercept: 3 4 (ii) Domain: all real numbers except 4 (iii) Vertical asymptote: x = 4; horizontal asymptote: y = 1 (iv) 8
y
4
-8
-4
8 x
4 -4 -8
D) (i) x intercept: 3; y intercept: 3 4 (ii) Domain: all real numbers except 4 (iii) Vertical asymptote: x = 4; horizontal asymptote: y = 1 (iv) 8
y
4
-8
-4
4
8 x
-4 -8
32
23) If a baseball player has a batting average of 0.420, what is the probability that the player will get at least 2 hits in the next four times at bat? A) 0.042 B) 0.333 C) 0.50 D) 0.559 Construct a pie graph, with sectors given in percent, to represent the data in the given table. 24) Age Number of people 25-35 294 35-45 396 45-55 348 55-65 186 65-75 90
A)
24)
B) 90%
7%
186%
294%
14%
22%
348%
396%
27%
30%
C)
D) 7%
10%
19%
22%
14%
24%
22%
30%
27%
26%
6
23)
Which single measure of central tendency - mean, median, or mode - would you say best describes the given set of measurements? 25) 2.02 1.93 2.24 3.56 1.98 25) 2.05 1.97 2.20 3.56 12.5 A) The Mean B) The Mode C) The Median Provide an appropriate response. 26) What proportion of the following sample of ten measurements lies within 2 standard deviations of the mean? 1 5 9 2 6 3 3 4 5 2 A) 90% B) 70% C) 80% D) 100%
26)
27) The life expectancy (in hours) of a fluorescent tube is normally distributed with mean 7,000 and standard deviation 1,000. Find the probability that a tube lasts for more than 8,900 hours. A) 0.0287 B) 0.9719 C) 0.9713 D) 0.0281
27)
28) Find the mean for the data set: 2, 11, 35, 2, 9, 35, 11, 9, 7, 2, 2, 2, 2, 9, 2 A) 11 B) 2
28) C) 9.33
D) 7
Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent. 29) A machine produces screws with an average diameter of 0.30 inches and a standard deviation of 29) 0.01 inches. What is the probability that a screw will have a diameter greater than 0.32 inches? A) 3% B) 1% C) 2% D) 97% Evaluate Cn,x pxqn-x for the given values of n, x, and p. 30) n = 6, x = 3, p = 1 6 A) 0.0286
30) B) 0.0322
C) 0.0536
D) 0.0154
Construct a pie graph, with sectors given in percent, to represent the data in the given table. 31) Favorite Beverage Number of responses Cola 340 Juice 210 Milk 230 Tea 310 Water 150
7
31)
A)
B)
150%
5% 340%
32%
310%
28% 210%
16%
230%
19%
C)
D)
8%
12% 24%
27%
28%
25% 21%
17%
19%
19%
Given a normal distribution with mean 120 and standard deviation 5, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. 32) 114.2 32) A) 2.4 B) 1.2 C) 2.12 D) 1.16 Construct a frequency table. 33) The following is the number of hours students studied per week on average. Use five intervals, starting with 0 - 4. 2 5
9 13 A)
14 19 17 24
20 21 15 13
18 10 5 4 9 14
2 19 B)
Interval Frequency 0-4 3 5-9 4 10-14 4 15-19 6 20-24 3
Interval Frequency 0-4 3 5-9 4 10-14 5 15-19 5 20-24 3
C)
D) Interval Frequency 0-4 3 5-9 4 10-14 5 15-19 4 20-24 4
Interval Frequency 0-4 3 5-9 3 10-14 6 15-19 5 20-24 3
8
33)
Provide an appropriate response. 34) Here are the commutes (in miles) for a group of six students. 14.7 16.3
34.0
33.7
22.6
34)
16.0
Find the range rounded to one decimal place. A) 16.0 B) 19.5
C) 34.0
D) 19.3
Given a normal distribution with mean 120 and standard deviation 5, find the number of standard deviations the measurement is from the mean. Express the answer as a positive number. 35) 107 35) A) 3.2 B) 2.6 C) 2 D) 1.4 Provide an appropriate response. 36) Following is a sample of the percent increases in the price of a house from 2000 to 2005 in 8 regions of the U. S. 75 130 145 150 150 225 225 300 Find the median. A) 150 B) 300 C) 137.5 D) 225
36)
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. 37) Two percent of flat irons produced at a certain plant are defective. Estimate the probability that 37) of 10,000 randomly selected flat irons, the number of defectives is between 195 and 210 inclusive. A) 0.4034 B) 0.3989 C) 0.4251 D) 0.4017 Provide an appropriate response. 38) The register of a college recorded the amount of time each student spent waiting in line during peak registration hours one Monday. The frequency table below summarizes the results. Find the standard deviation. Round your answer to one decimal place. Waiting time Number of (minutes) students 0-3 15 4-7 15 8 - 11 8 12 - 15 9 16 - 19 0 20 - 23 3 A) 5.4 B) 5.8
C) 5.9
D) 5.3
38)
E) 5.6
39) A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? A) 0.172 B) 0.117 C) 0.945 D) 0.055
39)
Evaluate Cn,x pxqn-x for the given values of n, x, and p. 40) n = 30, x = 12, p = 0.20 A) 0.1082
40) B) 0.0028
C) 0.0064
9
D) 0.0139