TEST BANK TRIGONOMETRY TWELFTH EDITION. Michael Sullivan by digitaldownload87

Sullivan Trigonometry: A Unite Circle Approach 12e Chapter 1 Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Name the quadrant in which the point is located. 1) (8, 4) A) I B) II

C) III

D) IV

C) III

D) IV

C) III

D) IV

C) III

D) IV

C) F and E

D) B and C

C) I and J

D) A and J

C) F, K, and L

D) B, F, and L

C) D and G

D) I and G

Objective: (1.1) Rectangular Coordinates

2) (-14, 3) A) I

B) II

Objective: (1.1) Rectangular Coordinates

3) (-15, -15) A) I

B) II

Objective: (1.1) Rectangular Coordinates

4) (20, -19) A) I

B) II

Objective: (1.1) Rectangular Coordinates

Identify the points in the graph for the ordered pairs. y B

E C G

-5

H J I

-5

5) (0, 2), (4, 3) A) C and E

B) C and K

Objective: (1.1) Rectangular Coordinates

6) (-5, -4), (0, -3) A) G and I

B) A and G

Objective: (1.1) Rectangular Coordinates

7) (-3, 4), (2, 0), (4, -5) A) B, C, and L

B) A, B, and F

Objective: (1.1) Rectangular Coordinates

8) (3, 5), (-3, 0) A) D and J

B) L and J

Objective: (1.1) Rectangular Coordinates

Give the coordinates of the points shown on the graph. 9) y

B 5 A -5

-5

A) A = (5, 1), B = (-3, 4) C) A = (1, 26), B = (4, -3)

B) A = (5, 1), B = (4, -3) D) A = (5, 4), B = (1, 4)

Objective: (1.1) Rectangular Coordinates

10) y C 5

-5

D -5

A) C = (-3, 7), D = (-3, 3) C) C = (-3, 7), D = (3, -3)

B) C = (-3, -3), D = (7, -3) D) C = (7, -3), D = (-3, 3)

Objective: (1.1) Rectangular Coordinates

11) y E

-5 F

-5

A) E = (-5, -5), F = (5, -5) C) E = (5, -5), F = (-5, -6)

B) E = (-6, -5) , F = (-5, 5) D) E = (-5, 5), F = (-6, -5)

Objective: (1.1) Rectangular Coordinates

12) y

5 G

-5

5 H -5

A) G = (2, 4), H = (-5, -2) C) G = (4, -5), H = (2, -5)

B) G = (4, 2), H = (-5, -2) D) G = (4, 2), H = (-2, -5)

Objective: (1.1) Rectangular Coordinates

Plot the point in the xy-plane. Tell in which quadrant or on what axis the point lies. 13) (6, 1) y 5

-5

B) y

-5

Quadrant II

Quadrant IV

D) y

-5

Quadrant I

Objective: (1.1) Rectangular Coordinates

14) (-5, 4) y 5

-5

B) y

-5

Quadrant IV

Quadrant II

-5

Quadrant I

Quadrant III

Objective: (1.1) Rectangular Coordinates

15) (2, -6) y 5

-5

B) y

-5

Quadrant III

Quadrant I

-5

Quadrant IV

Quadrant II

Objective: (1.1) Rectangular Coordinates

16) (-4, -6) y 5

-5

B) y

-5

Quadrant II

Quadrant IV

-5

Quadrant III

Objective: (1.1) Rectangular Coordinates

17) (0, 6) y 5

-5

B) y

-5

x-axis

y-axis

-5

Quadrant II

y-axis

Objective: (1.1) Rectangular Coordinates

18) (-5, 0) y 5

-5

B) y

-5

y-axis

x-axis

-5

Quadrant II

x-axis

Objective: (1.1) Rectangular Coordinates

Find the distance d(P1 , P2 ) between the points P1 and P2 . 19) 6

4 2

-6

-4

-2

6 x

-2 -4 -6

A) 2

C) 5

Objective: (1.1) Use the Distance Formula

D) 3

20) 8

6 4 2 -8

-6

-4

-2

8 x

185

-2 -4 -6 -8

A) 9

C) 3 17

D) 52

C) 2

D) 2 5

C) 27

D) 27 3

Objective: (1.1) Use the Distance Formula

21) 8

6 4 2 -8

-6

-4

-2

8 x

-2 -4 -6 -8

A) 12 3

B) 12

Objective: (1.1) Use the Distance Formula

22) 8

6 4 2 -8

-6

-4

-2

8 x

-2 -4 -6 -8

A) 3

B) 3 5

Objective: (1.1) Use the Distance Formula

23) P1 = (-3, -3); P2 = (-3, 5) A) 2 2

B) 7

C) 8

D) 9

C) 100

D) 20

C) 16

D) 2 5

C) 4

Objective: (1.1) Use the Distance Formula

24) P1 = (2, -3); P2 = (-4, 5) A) 11

B) 10

Objective: (1.1) Use the Distance Formula

25) P1 = (0, -2); P2 = (4, -2) A) 4

B) 2

Objective: (1.1) Use the Distance Formula

26) P1 = (0, 0); P2 = (-3, 7) A) 58

B) i 21

Objective: (1.1) Use the Distance Formula

27) P1 = (7, 5); P2 = (-7, -4) A)

115

B) 5

277

D) 126

Objective: (1.1) Use the Distance Formula

28) P1 = (2, -3); P2 = (6, -5) A) 12 3

B) 2 5

C) 6

D) 12

C) 60

D) 60 15

Objective: (1.1) Use the Distance Formula

29) P1 = (-6, -4); P2 = (2, -2) A) 2 17

B) 6

Objective: (1.1) Use the Distance Formula

30) P1 = (0.8, 0.4); P2 = (1.1, -2.8) Round to three decimal places, if necessary. A) 3.214

B) 10.164

C) 3.314

Objective: (1.1) Use the Distance Formula

Decide whether or not the points are the vertices of a right triangle. 31) (-8, 1), (-2, 1), (-2, 9) A) Yes

B) No

Objective: (1.1) Use the Distance Formula

32) (6, -5), (8, -1), (10, -2) A) Yes

B) No

Objective: (1.1) Use the Distance Formula

33) (-5, -7), (1, -5), (0, -10) A) Yes

B) No

Objective: (1.1) Use the Distance Formula

D) 17.5

34) (6, -5), (12, -3), (18, -10) A) Yes

B) No

Objective: (1.1) Use the Distance Formula

Solve the problem. 35) Find all values of k so that the given points are (-5, 5), (k, 0) A) 3, 7 B) -3, -7

29 units apart. C) 7

D) -7

Objective: (1.1) Use the Distance Formula

36) Find the area of the right triangle ABC with A = (-2, 7), B = (7, -1), C = (3, 9). 29 A) 29 square units B) square units C) 58 square units 2

58 square units 2

Objective: (1.1) Use the Distance Formula

37) Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10. A) (9, 13), (9, -7) B) (9, -12), (9, 8) C) (9, 2), (9, -4)

D) (9, 6), (9, -10)

Objective: (1.1) Use the Distance Formula

38) A middle school's baseball playing field is a square, 55 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. A) 77 feet B) 85 feet C) 78 feet D) 79 feet Objective: (1.1) Use the Distance Formula

39) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find an expression for their distance apart in miles at the end of t hours. A) 52t miles B) 52 t miles C) t 68 miles D) 2t 13 miles Objective: (1.1) Use the Distance Formula

40) A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To the nearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75 yards. A) 146 yards B) 145 yards C) 346 yards D) 345 yards Objective: (1.1) Use the Distance Formula

41) Find the length of each side of the triangle determined by the three points P1 , P2 , and P3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. P1 = (-5, -4), P2 = (-3, 4), P3 = (0, -1) A) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) = 5 2

right triangle B) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) = 5 2

neither C) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) =

isosceles triangle D) d(P1 , P2 ) = 2 17; d(P2 , P3 ) =

34; d(P1 , P3 ) =

both Objective: (1.1) Use the Distance Formula

Find the midpoint of the line segment joining the points P1 and P2 . 42) P1 = (5, 7); P2 = (9, 9) A) (7, 8)

B) (-4, -2)

C) (8, 7)

D) (14, 16)

C) 5, -11

D) -

C) -9, -15

C) (1, -0.8)

D) (0.5, -1.5)

Objective: (1.1) Use the Midpoint Formula

43) P1 = (1, -4); P2 = (-4, 7) A)

5 11 ,2 2

B) -3, 3

3 3 , 2 2

Objective: (1.1) Use the Midpoint Formula

44) P1 = (7, 1); P2 = (-16, -16) A) -

9 15 ,2 2

B) 9, 15

23 17 , 2 2

Objective: (1.1) Use the Midpoint Formula

45) P1 = (-0.5, -0.7); P2 = (1.5, -2.3) A) (-0.8, 1)

B) (-1.5, 0.5)

Objective: (1.1) Use the Midpoint Formula

46) P1 = (x, 1); P2 = (0, 8) A) x,

9 2

x 9 , 2 2

C) -

x ,7 2

D) x, 9

Objective: (1.1) Use the Midpoint Formula

47) P1 = (3x, 2); P2 = (4x, 1) A)

3x 7 , 2 2

B) x, 1

C) 7x, 3

7x 3 , 2 2

Objective: (1.1) Use the Midpoint Formula

Solve the problem. 48) If (1, 3) is the endpoint of a line segment, and (3, 8) is its midpoint, find the other endpoint. A) (-3, -7) B) (11, 7) C) (5, 13) D) (5, -2) Objective: (1.1) Use the Midpoint Formula

49) If (-3, 2) is the endpoint of a line segment, and (-7, 0) is its midpoint, find the other endpoint. A) (5, 6) B) (-11, 4) C) (-7, -6) D) (-11, -2) Objective: (1.1) Use the Midpoint Formula

50) If (1, 2) is the endpoint of a line segment, and (2, -1) is its midpoint, find the other endpoint. A) (3, 5) B) (-1, 8) C) (3, -4) D) (-5, 4) Objective: (1.1) Use the Midpoint Formula

51) If (-2, -3) is the endpoint of a line segment, and (-7, 1) is its midpoint, find the other endpoint. A) (6, -13) B) (-12, 5) C) (8, -11) D) (-12, -7) Objective: (1.1) Use the Midpoint Formula

52) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two-thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0). 17 8 2 17 A) B) 2 C) D) 3 3 3 Objective: (1.1) Use the Midpoint Formula

Determine whether the given point is on the graph of the equation. 53) Equation: y = x3 - x Point: (1, 0) A) No

B) Yes

Objective: (1.2) Graph Equations by Plotting Points

54) Equation: x 2 + y2 = 4 Point: (2, 0) A) No

B) Yes

Objective: (1.2) Graph Equations by Plotting Points

Graph the equation by plotting points. 55) y = x + 1 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Graph Equations by Plotting Points

56) y = 2x + 4 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Graph Equations by Plotting Points

57) y = x2 - 4 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Graph Equations by Plotting Points

58) 2x + 4y = 8 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Graph Equations by Plotting Points

59) x2 + 9y = 9 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Graph Equations by Plotting Points

Solve the problem. 60) If (a, 3) is a point on the graph of y = 2x - 5, what is a? A) -1 B) 1

C) -4

D) 4

C) 4

Objective: (1.2) Graph Equations by Plotting Points

61) If (3, b) is a point on the graph of 3x - 2y = 17, what is b? 23 A) B) -4 3

11 3

Objective: (1.2) Graph Equations by Plotting Points

62) The height of a baseball (in feet) at time t (in seconds) is given by y = -16x2 + 80x + 5. Which one of the following points is not on the graph of the equation? A) (3, 101) B) (2, 117) C) (1, 69) D) (4, 69) Objective: (1.2) Graph Equations by Plotting Points

List the intercepts of the graph. 63) y 10

-10

-5

-10

A) (-1, 0), (1, 0)

B) (0, -1), (1, 0)

C) (-1, 0), (0, 1)

Objective: (1.2) Find Intercepts from a Graph

D) (0, -1), (0, 1)

64) y 5

-5

A) (0, 0)

B) (0, 1)

C) (1, 1)

D) (1, 0)

Objective: (1.2) Find Intercepts from a Graph

65) y 5 4 3 2 1 -

- 2

-1 -2

 2



-3 -4 -5

A) -

π π , 0 , (-2, 0), ,0 2 2

B) 0, -

π π , (0, -2), 0, 2 2

C) -

π π , 0 , (0, -2), ,0 2 2

D) 0, -

π π , (-2, 0), 0, 2 2

Objective: (1.2) Find Intercepts from a Graph

66) y 10

-10

-5

-10

A) (0, -2), (0, 8), (4, 0)

B) (-2, 0), (0, 8), (4, 0)

C) (0, -2), (8, 0), (0, 4)

D) (-2, 0), (0, 8), (0, 4)

C) (0, 2)

D) (-2, 0)

Objective: (1.2) Find Intercepts from a Graph

67) y 10

-10

-5

-10

A) (2, 0)

B) (0, -2)

Objective: (1.2) Find Intercepts from a Graph

68) y 10

-10

-5

-10

A) (-4, 0), (0, -4), (0, 4), (4, 0) C) (-4, 0), (0, -4), (0, 0), (0, 4), (4, 0)

B) (0, 4), (4, 0) D) (-4, 0), (0, 4)

Objective: (1.2) Find Intercepts from a Graph

69) y 10

-10

-5

-10

A) (3, 0), (1, 0), (-5, 0), (0, 3) C) (-3, 0), (1, 0) (5, 0), (0, 3)

B) (3, 0), (0, 3), (0, 1), (0, -5) D) (3, 0), (0, -3), (0, 1), (0, 5)

Objective: (1.2) Find Intercepts from a Graph

70)

A) (-2, 0), (0, 4), (2, 0)

B) (-2, 0), (0, 2), (2, 0)

C) (-4, 0), (0, 4), (4, 0)

D) (-2, 0), (2, 0)

C) (-5, 0), (0, -5)

D) (-5, 0), (0, 5)

C) (0, 0)

D) (2, 0)

C) (-1, 0), (0, -1), (1, 0)

D) (0, -1), (1, 0), (0, 1)

Objective: (1.2) Find Intercepts from a Graph

List the intercepts for the graph of the equation. 71) y = x + 5 A) (5, 0), (0, 5) B) (5, 0), (0, -5) Objective: (1.2) Find Intercepts from an Equation

72) y = 2x A) (2, 2)

B) (0, 2)

Objective: (1.2) Find Intercepts from an Equation

73) y2 = x + 1 A) (1, 0), (0, 1), (0, -1)

B) (0, -1), (-1, 0), (0, 1)

Objective: (1.2) Find Intercepts from an Equation

9 74) y = x A) (1, 0)

B) (0, 1)

C) (1, 1)

D) (0, 0)

C) (-2, 0), (0, -4), (2, 0)

D) (2, 0), (0, 4), (0, -4)

Objective: (1.2) Find Intercepts from an Equation

75) x2 + y - 4 = 0 A) (0, -2), (4, 0), (0, 2)

B) (-2, 0), (0, 4), (2, 0)

Objective: (1.2) Find Intercepts from an Equation

76) 4x2 + 9y2 = 36 A) (-2, 0), (-3, 0), (3, 0), (2, 0) C) (-3, 0), (0, -2), (0, 2), (3, 0)

B) (-4, 0), (-9, 0), (9, 0), (4, 0) D) (-9, 0), (0, -4), (0, 4), (9, 0)

Objective: (1.2) Find Intercepts from an Equation

77) 9x2 + y2 = 9 A) (-9, 0), (0, -1), (0, 1), (9, 0) C) (-1, 0), (0, -9), (0, 9), (1, 0)

B) (-3, 0), (0, -1), (0, 1), (3, 0) D) (-1, 0), (0, -3), (0, 3), (1, 0)

Objective: (1.2) Find Intercepts from an Equation

78) y = x 3 - 125 A) (0, -5), (0, 5)

B) (0, -5), (-5, 0)

C) (0, -125), (5, 0)

D) (-125, 0), (0, 5)

C) (0, 1)

D) (0, -1), (-1, 0), (1, 0)

C) (0, -2), (0, -3), (6, 0)

D) (-2, 0), (-3, 0), (0, 6)

C) (16, 0)

D) (0, 16)

Objective: (1.2) Find Intercepts from an Equation

79) y = x 4 - 1 A) (0, -1)

B) (0, 1), (-1, 0), (1, 0)

Objective: (1.2) Find Intercepts from an Equation

80) y = x2 + 5x + 6 A) (0, 2), (0, 3), (6, 0)

B) (2, 0), (3, 0), (0, 6)

Objective: (1.2) Find Intercepts from an Equation

81) y = x 2 + 16 A) (16, 0), (0, -4), (0, 4)

B) (0, 16), (-4, 0), (4, 0)

Objective: (1.2) Find Intercepts from an Equation

82) y =

7x 2 x + 49

A) (-7, 0), (0, 0), (7, 0) C) (0, -7), (0, 0), (0, 7)

B) (-49, 0), (0, 0), (49, 0) D) (0, 0)

Objective: (1.2) Find Intercepts from an Equation

83) y =

x2 - 25 5x4

A) (-5, 0), (5, 0) C) (0, -5), (0, 5)

B) (0, 0) D) (-25, 0), (0, 0), (25, 0)

Objective: (1.2) Find Intercepts from an Equation

Plot the point A. Plot the point B that has the given symmetry with point A. 23

84) A = (-2, 3); B is symmetric to A with respect to the x-axis 5

4 3 2 1 -5

-4

-3

-2

-1

-2 -3 -4 -5

B) 5

-5

-4

-3

-2

-1

1 1

-1

-5

-4

-3

-2

-1

-2

-3

-4

-5

D) 5

1 -5

-4

-3

-2

-1

1 1

-5

-4

-3

-2

-1

-2

-3

-4

-5

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

85) A = (0, -1); B is symmetric to A with respect to the origin 5

4 3 2 1 -5

-4

-3

-2

-1

-2 -3 -4 -5

B) 5

B -5

-4

-3

-2

-1 A -1

-5

-4

-3

-2

-1

B -1

-2

-3

-4

-5

D) 5

2 B 1

1 B

-5

-4

-3

-2

-1 A -1

-5

-4

-3

-2

-1 A -1

-2

-3

-4

-5

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

List the intercepts of the graph.Tell whether the graph is symmetric with respect to the x-axis, y-axis, origin, or none of these. 86) y 10

-10

-5

-10

A) intercepts: (0, -3) and (0, 3) symmetric with respect to y-axis B) intercepts: (-3, 0) and (3, 0) symmetric with respect to x-axis, y-axis, and origin C) intercepts: (0, -3) and (0, 3) symmetric with respect to x-axis, y-axis, and origin D) intercepts: (-3, 0) and (3, 0) symmetric with respect to origin Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

87) y 10

-10

-5

-10

A) intercepts: (0, 3) and (0, -3) symmetric with respect to x-axis, y-axis, and origin B) intercepts: (0, 3) and (0, -3) symmetric with respect to origin C) intercepts: (3, 0) and (-3, 0 symmetric with respect to y-axis D) intercepts: (3, 0) and (-3, 0) symmetric with respect to x-axis, y-axis, and origin Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

88) y 10

-10

-5

-10

A) intercept: (7, 0) symmetric with respect to y-axis C) intercept: (7, 0) no symmetry

B) intercept: (0, 7) symmetric with respect to x-axis D) intercept: (0, 7) no symmetry

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

89) y 10

-10

-5

-10

A) intercept: (6, 0) symmetric with respect to y-axis C) intercept: (0, 6) symmetric with respect to origin

B) intercept: (0, 6) symmetric with respect to y-axis D) intercept: (6, 0) symmetric with respect to x-axis

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

90) y 10

-10

-5

-10

A) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to origin B) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to x-axis C) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to x-axis, y-axis, and origin D) intercepts: (-3, 0), (0, 0), (3, 0) symmetric with respect to y-axis Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

Draw a complete graph so that it has the given type of symmetry. 91) Symmetric with respect to the y-axis 5 (0, 4) 4

3 2 1 (2, 0) -5

-4

-3

-2

-1

5 x

-2 -3 -4 -5

B) 5

-5

-4

-3

-2

-1

1 1

-1

5 x

-5

-4

-3

-2

-1

-2

-3

-4

-5

5 x

D) 5

-5

-4

-3

-2

-1

1 1

-1

5 x

-5

-4

-3

-2

-1

-2

-3

-4

-5

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

92) origin 5

4 3 2 1 -

- 2

-1

 2



-2 -3 -4 -5

B) y

- 2

-

1  2

-1



-

- 2

-1

-2

-3

-4

-5

 2



 2



D) y

- 2

-

1  2

-1



-

- 2

-1

-2

-3

-4

-5

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

93) Symmetric with respect to the x-axis 5

4 3 2 (3, 1)

(2, 0) -5

-4

-3

-2

-1

5 x

-2 -3 -4 -5

B) 5

-5

-4

-3

-2

-1

1 1

-1

5 x

-5

-4

-3

-2

-1

-2

-3

-4

-5

5 x

D) 5

-5

-4

-3

-2

-1

5 x

-5

-4

-3

-2

-1

-2

-3

-4

-5

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

List the intercepts and type(s) of symmetry, if any. 94) y2 = x + 1 A) intercepts: (1, 0), (0, 1), (0, -1) symmetric with respect to x-axis C) intercepts: (0, 1), (1, 0), (-1, 0) symmetric with respect to y-axis

B) intercepts: (-1, 0), (0, 1), (0, -1) symmetric with respect to x-axis D) intercepts: (0, -1), (1, 0), (-1, 0) symmetric with respect to y-axis

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

95) 16x2 + 9y2 = 144 A) intercepts: (3, 0), (-3, 0), (0, 4), (0, -4) symmetric with respect to x-axis, y-axis, and origin B) intercepts: (3, 0), (-3, 0), (0, 4), (0, -4) symmetric with respect to x-axis and y-axis C) intercepts: (4, 0), (-4, 0), (0, 3), (0, -3) symmetric with respect to x-axis and y-axis D) intercepts: (4, 0), (-4, 0), (0, 3), (0, -3) symmetric with respect to the origin Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

96) y =

-x 2 x -7

A) intercept: (0, 0) symmetric with respect to y-axis C) intercept: (0, 0) symmetric with respect to origin

B) intercept: (0, 0) symmetric with respect to x-axis D) intercepts: ( 7, 0), (- 7, 0), (0, 0) symmetric with respect to origin

Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin. 97) y = x - 2 A) origin B) x-axis C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

98) y = -2x A) y-axis B) origin C) x-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

99) x2 + y - 25 = 0 A) y-axis B) origin C) x-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

100) y2 - x - 81 = 0 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

101) 4x2 + 9y2 = 36 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

102) 16x2 + y2 = 16 A) origin B) y-axis C) x-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

103) y = x2 + 7x + 10 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

104) y =

6x x2 + 36

A) y-axis B) x-axis C) origin D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

105) y =

x2 - 36 6x4

A) y-axis B) origin C) x-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

106) y = 2x2 - 3 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

107) y = (x - 8)(x + 5) A) y-axis B) x-axis C) origin D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

108) y = -6x3 + 4x A) x-axis B) y-axis C) origin D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

109) y = 4x4 - 9x - 7 A) x-axis B) origin C) y-axis D) x-axis, y-axis, origin E) none Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

Solve the problem. 110) If a graph is symmetric with respect to the y-axis and it contains the point (5, -6), which of the following points is also on the graph? A) (-5, -6) B) (-5, 6) C) (-6, 5) D) (5, -6) Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

111) If a graph is symmetric with respect to the origin and it contains the point (-4, 7), which of the following points is also on the graph? A) (-4, -7) B) (4, -7) C) (4, 7) D) (7, -4) Objective: (1.2) Test an Equation for Symmetry with Respect to the x-Axis, the y-Axis, and the Origin

Graph the equation by plotting points. 112) y = x 3 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Know How to Graph Key Equations

113) x = y2 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

x y 10

-10

-5

Objective: (1.2) Know How to Graph Key Equations

114) y =

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.2) Know How to Graph Key Equations

115) y =

1 x y 5

-5

B) y

-5

D) y

-5

Objective: (1.2) Know How to Graph Key Equations

Find the slope of the line through the points and interpret the slope. 116) y 10

5 (11, 1)

(0, 0) -10

-5

-10

A) -11; for every 1-unit increase in x, y will decrease by 11 units B) 11; for every 1-unit increase in x, y will increase by 11 units 1 C) ; for every 11-unit increase in x, y will increase by 1 unit 11 D) -

1 ; for every 11-unit increase in x, y will decrease by 1 unit 11

Objective: (1.3) Calculate and Interpret the Slope of a Line

Find the slope of the line. 117) y 10

-10

-5

-10

A) -

1 10

B) 10

1 10

C) - 10

C) -1

D) 5

C) -1

D) -3

Objective: (1.3) Calculate and Interpret the Slope of a Line

118) y 10

-10

-5

-10

A) -5

B) 1

Objective: (1.3) Calculate and Interpret the Slope of a Line

119) y 10

-10

-5

-10

A) 1

B) 3

Objective: (1.3) Calculate and Interpret the Slope of a Line

120) y 10

-10

-5

-10

A) -5

1 5

C) -

1 5

D) 5

C) -

6 11

11 6

5 4

Objective: (1.3) Calculate and Interpret the Slope of a Line

Find the slope of the line containing the two points. 121) (2, -7); (-4, 4) 6 11 A) B) 11 6 Objective: (1.3) Calculate and Interpret the Slope of a Line

122) (5, 0); (0, 4) 5 A) 4

B) -

4 5

1 11

D) 11

Objective: (1.3) Calculate and Interpret the Slope of a Line

123) (-5, -6); (-4, 5) 1 A) 11

B) - 11

Objective: (1.3) Calculate and Interpret the Slope of a Line

124) (-9, 7); (-9, 8) A) 0

B) 1

C) - 1

D) undefined

C) -12

D) undefined

Objective: (1.3) Calculate and Interpret the Slope of a Line

125) (5, -4); (-7, -4) 1 A) 12

B) 0

Objective: (1.3) Calculate and Interpret the Slope of a Line

Graph the line containing the point P and having slope m.

126) P = (-2, 7); m = -

2 3 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

127) P = (-3, 0); m = 2 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

128) P = (-5, -8); m = -

3 2 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

129) P = (0, 3); m =

1 3 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

130) P = (0, 6); m = -

4 5 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

131) P = (-3, 0); m =

3 2 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

132) P = (4, 0); m = -

2 3 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

133) P = (3, 8); m = 0 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

134) P = (5, -9); slope undefined y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.3) Graph Lines Given a Point and the Slope

Find an equation for the line with the given properties. 135) Slope undefined; containing the point (-2, -4) A) y = -2 B) x = -2

C) y = -4

D) x = -4

C) y = -7

D) x = -2

Objective: (1.3) Find the Equation of a Vertical Line

136) Vertical line; containing the point (-7, -2) A) x = -7 B) y = -2 Objective: (1.3) Find the Equation of a Vertical Line

137) Slope undefined; containing the point A) y = -

4 5

4 ,5 5

B) y = 5

C) x = -

4 5

D) x = 5

Objective: (1.3) Find the Equation of a Vertical Line

138) Vertical line; containing the point (-2.2, -4.0) A) x = -2.2 B) x = 0

C) x = -4.0

D) x = 6.2

Find the slope-intercept form of the equation of the line with the given properties. 139) Horizontal; containing the point (10, -10) A) x = 10 B) y = -10 C) y = 10

D) x = -10

Objective: (1.3) Find the Equation of a Vertical Line

Objective: (1.3) Use the Point-Slope Form of a Line; Identify Horizontal Lines

140) Slope = 0; containing the point (-10, -8) A) y = -8 B) x = -8

C) x = -10

D) y = -10

Objective: (1.3) Use the Point-Slope Form of a Line; Identify Horizontal Lines

141) Horizontal; containing the point A) y = -

3 4

3 ,5 4

B) y = 0

C) y = 5

D) y = -5

Objective: (1.3) Use the Point-Slope Form of a Line; Identify Horizontal Lines

142) Horizontal; containing the point (5.8, -1.7) A) y = 0 B) y = -1.7

C) y = 5.8

Objective: (1.3) Use the Point-Slope Form of a Line; Identify Horizontal Lines

Find the slope of the line and sketch its graph. 143) y + 3 = 0 y 10

-10

-5

-10

D) y = 4.1

A) slope = -3

B) slope is undefined y

-10

-5

C) slope = -

-10

-5

-10

1 3

D) slope = 0 y y

10 5 5

-10

-5

-10

-5 -5

-5 -10 -10

Objective: (1.3) Use the Point-Slope Form of a Line; Identify Horizontal Lines

Find the equation of the line in slope-intercept form. 144) 6

4 2

-6

-4

-2

6 x

-2 -4 -6

A) y = 3x + 10

B) y = 3x - 10

C) y =

Objective: (1.3) Find the Equation of a Line Given Two Points

1 2 x+ 3 5

D) y = 3x + 6

Find an equation for the line, in the indicated form, with the given properties. 145) Containing the points (-1, 5) and (4, -6); slope-intercept form 11 14 14 11 14 A) y = x+ B) y = mx + C) y = x+ 5 5 5 5 5

D) y - 5 = -

11 (x + 1) 5

Objective: (1.3) Find the Equation of a Line Given Two Points

146) Containing the points (1, -5) and (-4, 4); general form A) 6x - 8y = -8 B) -6x + 8y = -8

C) 9x + 5y = -16

D) -9x + 5y = -16

Objective: (1.3) Find the Equation of a Line Given Two Points

147) Containing the points (6, 0) and (0, -5); general form 5 A) y = - x - 5 B) 5x - 6y = 30 6

5 x+6 6

D) 5x + 6y = 30

C) 3x + 2y = -12

D) 13x - 12y = 32

C) -16x + 6y = -36

D) 16x - 6y = -36

C) 5x + 9y = -10

D) -5x + 9y = -10

C) -3x - 13y = 11

D) 3x - 13y = 11

C) y = -

Objective: (1.3) Find the Equation of a Line Given Two Points

148) Containing the points (-4, -7) and (8, 6); general form A) -13x - 12y = 32 B) -3x - 2y = -12 Objective: (1.3) Find the Equation of a Line Given Two Points

149) Containing the points (-7, 9) and (0, -6); general form A) -15x - 7y = 42 B) 15x - 7y = 42 Objective: (1.3) Find the Equation of a Line Given Two Points

150) Containing the points (2, 0) and (-7, -5); general form A) -2x + 2y = 24 B) 2x - 2y = 24 Objective: (1.3) Find the Equation of a Line Given Two Points

151) Containing the points (-8, 1) and (5, -2); general form A) 9x - 7y = 31 B) -9x + 7y = 31 Objective: (1.3) Find the Equation of a Line Given Two Points

Solve. 152) The relationship between Celsius (°C) and Fahrenheit (°F) degrees of measuring temperature is linear. Find an equation relating °C and °F if 10°C corresponds to 50°F and 30°C corresponds to 86°F. Use the equation to find the Celsius measure of 1° F. 5 160 155 9 391 A) C = F ; °C B) C = F - 80; °C 9 9 9 5 5 C) C =

5 85 F - 10; °C 9 9

D) C =

Objective: (1.3) Find the Equation of a Line Given Two Points

5 160 55 F+ ; °C 9 9 3

153) A school has just purchased new computer equipment for $22,000.00. The graph shows the depreciation of the equipment over 5 years. The point (0, 22,000) represents the purchase price and the point (5, 0) represents when the equipment will be replaced. Write a linear equation in slope-intercept form that relates the value of the equipment, y, to years after purchase x . Use the equation to predict the value of the equipment after 1 years. 25000

22500 20000 17500 15000 12500 10000 7500 5000 2500 2.5

A) y = - 22,000x + 22,000; value after 1 years is $0.00 C) y = 4400x - 22,000; value after 1 years is $17,600.00

B) y = 22,000x + 5; value after 1 years is $17,600.00 D) y = - 4400x + 22,000; value after 1 years is $17,600.00;

Objective: (1.3) Find the Equation of a Line Given Two Points

154) The average value of a certain type of automobile was $13,980 in 1,994 and depreciated to $4,980 in 1,997. Let y be the average value of the automobile in the year x, where x = 0 represents 1,994. Write a linear equation that relates the average value of the automobile, y, to the year x. 1 A) y = -3,000x + 4,980 B) y = -3,000x - 4,020 C) y = x - 4980 D) y = -3,000x + 13,980 3000 Objective: (1.3) Find the Equation of a Line Given Two Points

155) An investment is worth $2,806 in 1,993. By 1,997 it has grown to $4,622. Let y be the value of the investment in the year x, where x = 0 represents 1,993. Write a linear equation that relates the value of the investment, y, to the year x. 1 A) y = x + 2,806 B) y = -454x + 6,438 C) y = -454x + 2,806 D) y = 454x + 2,806 454 Objective: (1.3) Find the Equation of a Line Given Two Points

156) A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 4 seconds, the gauge on the bottle indicates that it contains 10 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 24 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that relates the amount of water in the bottle,y, to the time x. 1 A) y = -2x + 18 B) y = x + 8 C) y = 2x + 13 D) y = 2x + 2 2 Objective: (1.3) Find the Equation of a Line Given Two Points

157) When making a telephone call using a calling card, a call lasting 3 minutes cost $0.80. A call lasting 10 minutes cost $1.50. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that relates the cost of a making a call, y, to the time x. 146 A) y = 0.1x + 0.5 B) y = -0.1x + 1.1 C) y = 0.1x - 8.5 D) y = 10x 5 Objective: (1.3) Find the Equation of a Line Given Two Points

158) A vendor has learned that, by pricing carmel apples at $1.25, sales will reach 120 carmel apples per day. Raising the price to $2.25 will cause the sales to fall to 72 carmel apples per day. Let y be the number of carmel apples the vendor sells at x dollars each. Write a linear equation that relates the number of carmel apples sold per day, y, to the price x. 1 23035 A) y = -48x - 180 B) y = x+ C) y = 48x + 60 D) y = -48x + 180 48 192 Objective: (1.3) Find the Equation of a Line Given Two Points

159) A vendor has learned that, by pricing caramel apples at $1.00, sales will reach 98 caramel apples per day. Raising the price to $2.00 will cause the sales to fall to 54 caramel apples per day. Let y be the number of caramel apples the vendor sells at x dollars each. Write a linear equation that relates the number of caramel apples sold per day to the price x. 1 4311 A) y = -44x - 142 B) y = 44x + 54 C) y = -44x + 142 D) y = x+ 44 44 Objective: (1.3) Find the Equation of a Line Given Two Points

Find the slope-intercept form of the equation of the line with the given properties. 160) Slope = 5; containing the point (-3, -10) A) y = 5x + 5 B) y = -5x + 5 C) y = 5x - 5

D) y = -5x - 5

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

161) Slope = 0; containing the point (-2, -5) A) x = -2 B) y = -5

C) y = -2

D) x = -5

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

162) Slope = -9; y-intercept = 20 A) y = -9x + 20

B) y = -9x - 20

C) y = 20x - 9

D) y = 20x + 9

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

163) x-intercept = 8; y-intercept = 5 5 5 A) y = x + 5 B) y = - x + 8 8 8

C) y = -

5 x+5 8

D) y = -

8 x+8 5

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

Write the equation in slope-intercept form. 164) 16x + 7y = 13 16 13 16 13 A) y = x+ B) y = x7 7 7 7

C) y =

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

16 13 x+ 7 7

D) y = 16x - 13

165) 4x + 7y = 9 A) y = 4x + 12

B) y =

12 9 x+ 7 7

4 9 x+ 7 7

D) y =

7 9 x4 4

C) y = 5x - 4

D) y =

5 4 x+ 7 7

D) y =

1 x-4 9

C) y =

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

166) 5x - 7y = 4 5 4 A) y = x 7 7

B) y =

7 4 x+ 5 5

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

167) x = 9y + 4 A) y = x -

4 9

B) y =

1 4 x9 9

C) y = 9x - 4

Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

Solve. 168) A truck rental company rents a moving truck one day by charging $25 plus $0.07 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 130 miles? A) C = 0.07x + 25; $34.10 B) C = 0.07x + 25; $25.91 C) C = 25x + 0.07; $3,250.07 D) C = 0.07x - 25; $15.90 Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

169) Each week a soft drink machine sells x cans of soda for $0.75/soda. The cost to the owner of the soda machine for each soda is $0.10. The weekly fixed cost for maintaining the soda machine is $25/week. Write an equation that relates the weekly profit, P, in dollars to the number of cans sold each week. Then use the equation to find the weekly profit when 92 cans of soda are sold in a week. A) P = 0.65x - 25; $34.80 B) P = 0.75x + 25; $94.00 C) P = 0.75x - 25; $44.00 D) P = 0.65x + 25; $84.80 Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

170) Each day the commuter train transports x passengers to or from the city at $1.75/passenger. The daily fixed cost for running the train is $1200. Write an equation that relates the daily profit, P, in dollars to the number of passengers each day. Then use the equation to find the daily profit when the train has 920 passengers in a day. A) P = 1200 - 1.75x; $410 B) P = 1.75x; $1610 C) P = 1.75x + 1200; $2810 D) P = 1.75x - 1200; $410 Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

171) Each month a beauty salon gives x manicures for $12.00/manicure. The cost to the owner of the beauty salon for each manicure is $7.35. The monthly fixed cost to maintain a manicure station is $120.00. Write an equation that relates the monthly profit, in dollars, to the number of manicures given each month. Then use the equation to find the monthly profit when 200 manicures are given in a month. A) P =12x - 120; $2280 B) P = 4.65x; $930 C) P = 7.35x - 120; $1350 D) P = 4.65x - 120; $810 Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

172) Each month a gas station sells x gallons of gas at $1.92/gallon. The cost to the owner of the gas station for each gallon of gas is $1.32. The monthly fixed cost for running the gas station is $37,000. Write an equation that relates the monthly profit, in dollars, to the number of gallons of gasoline sold. Then use the equation to find the monthly profit when 75,000 gallons of gas are sold in a month. A) P = 1.32x - 37,000; $62,000 B) P = 0.60x + 37,000; $82,000 C) P = 1.92x - 37,000; $107,000 D) P = 0.60x - 37,000; $8000 Objective: (1.3) Write the Equation of a Line in Slope-Intercept Form

Find the slope and y-intercept of the line. 1 173) y = - x - 2 9 A) slope = - 2; y-intercept = -

1 9

B) slope = -

C) slope = - 9; y-intercept = 2

D) slope =

1 ; y-intercept = - 2 9

1 ; y-intercept = 2 9

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

174) x + y = 2 A) slope = -1; y-intercept = 2 C) slope = 0; y-intercept = 2

B) slope = -1; y-intercept = -2 D) slope = 1; y-intercept = 2

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

175) 12x + y = 8 A) slope = 12; y-intercept = 8 C) slope =

B) slope = -

3 1 ; y-intercept = 2 8

2 1 ; y-intercept = 3 12

D) slope = -12; y-intercept = 8

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

176) -6x + 5y = 8 A) slope =

12 8 ; y-intercept = 5 5

B) slope =

5 8 ; y-intercept = 6 6

C) slope =

6 8 ; y-intercept = 5 5

D) slope = 6; y-intercept = 12

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

177) 10x + 3y = 7 A) slope = C) slope =

10 7 ; y-intercept = 3 3

B) slope = 10; y-intercept = 7

10 7 ; y-intercept = 3 3

D) slope =

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

10 7 ; y-intercept = 3 3

178) 2x - 9y = 5

9 5 ; y-intercept = 2 2

B) slope =

2 5 ; y-intercept = 9 9

C) slope = 2; y-intercept = 5

D) slope =

2 5 ; y-intercept = 9 9

A) slope =

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

179) 3x - 12y = 36 A) slope =

1 ; y-intercept = -3 4

B) slope = 3; y-intercept = 36

1 ; y-intercept = 3 4

D) slope = 4; y-intercept = 12

C) slope = -

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

180) x + 5y = 1 A) slope =

1 1 ; y-intercept = 5 5

C) slope = -

B) slope = -5; y-intercept = 5

1 1 ; y-intercept = 5 5

D) slope = 1; y-intercept = 1

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

181) -x + 6y = 48 A) slope = -

1 ; y-intercept = 8 6

B) slope =

C) slope = 6; y-intercept = -48

1 ; y-intercept = 8 6

D) slope = -1; y-intercept = 48

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

182) y = -4 A) slope = 0; y-intercept = -4 C) slope = -4; y-intercept = 0

B) slope = 0; no y-intercept D) slope = 1; y-intercept = -4

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

183) x = -3 A) slope undefined; y-intercept = -3 C) slope undefined; no y-intercept

B) slope = -3; y-intercept = 0 D) slope = 0; y-intercept = -3

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

184) y = -6x A) slope = -6; y-intercept = 0

B) slope = 0; y-intercept = -6

1 ; y-intercept = 0 6

D) slope = 6; y-intercept = 0

C) slope = -

Objective: (1.3) Identify the Slope and y-Intercept of a Line from Its Equation

Find the general form of the equation for the line with the given properties. 3 6 185) Slope = ; y-intercept = 5 5 A) y =

3 6 x+ 5 5

B) 3x - 5y = -6

3 6 x5 5

D) 3x + 5y = -6

C) 5x + 6y = 27

D) 5x - 6y = 27

C) y =

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

186) Slope = -

5 ; containing the point (3, 2) 6

A) 6x + 5y = -27

B) 5x + 6y = -27

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

187) Slope = -

3 ; containing the point (0, 4) 4

A) 3x + 4y = -16

B) 4x + 3y = -16

C) 3x + 4y = 16

D) 3x - 4y = 16

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

188) Slope =

2 ; containing (0, 4) 9

A) -2x - 9y = 36

B) -2x + 9y = 36

C) 9x - 2y = -36

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

Find the slope of the line and sketch its graph. 189) 4x + 5y = 23 y 10

-10

-5

-10

D) -2x + 9y = -36

A) slope = -

5 4

B) slope =

5 4

-10

C) slope =

-5

-10

-5

-10

4 5

D) slope = -

-5

-10

-5

-10

190) 3x - 5y = -14 y 10

-5

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

-10

4 5

-10

-5

-10

A) slope = -

5 3

B) slope = -

3 5

-10

C) slope =

-5

-10

-5

-10

5 3

D) slope =

-5

3 5

-10

-5

-10

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

Solve the problem. 191) Find an equation in general form for the line graphed on a graphing utility.

A) y = -2x - 1

B) 2x + y = -1

C) y = -

Objective: (1.3) Graph Lines Written in General Form Using Intercepts

1 x-1 2

D) x + 2y = -2

Find an equation for the line with the given properties. 192) The solid line L contains the point (2, 1) and is parallel to the dotted line whose equation is y = 2x. Give the equation for the line L in slope-intercept form. y 5

-5

A) y = 2x - 3

B) y - 1 = 2(x - 2)

C) y = 2x - 1

D) y = 2x + b

C) y = -3x - 21

D) y - 6 = -3x - 5

Objective: (1.3) Find Equations of Parallel Lines

193) Parallel to the line y = -3x; containing the point (5, 6) A) y = -3x + 21 B) y = -3x Objective: (1.3) Find Equations of Parallel Lines

194) Parallel to the line x + 3y = 5; containing the point (0, 0) 4 1 A) y = B) y = - x 3 3

C) y = -

1 x+5 3

D) y =

1 x 3

D) y =

1 x 2

Objective: (1.3) Find Equations of Parallel Lines

195) Parallel to the line -2x - y = 6; containing the point (0, 0) 1 A) y = -2x B) y = - x 2

C) y =

1 x+6 2

Objective: (1.3) Find Equations of Parallel Lines

196) Parallel to the line y = -7; containing the point (6, 2) A) y = -7 B) y = -2

C) y = 6

D) y = 2

C) y = -6

D) y = 4

C) 6x + 7y = 22

D) 7x + 6y = -2

C) -3x + 2y = -12

D) -2x - 3y = -8

Objective: (1.3) Find Equations of Parallel Lines

197) Parallel to the line x = -6; containing the point (2, 4) A) x = 4 B) x = 2 Objective: (1.3) Find Equations of Parallel Lines

198) Parallel to the line 6x + 7y = -6; containing the point (6, -2) A) 6x - 7y = 22 B) 6x + 7y = -6 Objective: (1.3) Find Equations of Parallel Lines

199) Parallel to the line -2x - 3y = 4; x-intercept = 4 A) -3x + 2y = 8 B) -2x - 3y = -12 Objective: (1.3) Find Equations of Parallel Lines

200) The solid line L contains the point (4, 2) and is perpendicular to the dotted line whose equation is y = 2x. Give the equation of line L in slope-intercept form. y 5

-5

A) y - 2 = 2(x - 4)

B) y - 2 = -

1 (x - 4) 2

C) y =

1 x+4 2

D) y = -

1 x+4 2

Objective: (1.3) Find Equations of Perpendicular Lines

201) Perpendicular to the line y = 4x - 1; containing the point (-1, 4) 1 1 15 15 15 A) y = - x + B) y = -4x + C) y = x + 4 4 4 4 4

D) y = 4x +

15 4

Objective: (1.3) Find Equations of Perpendicular Lines

202) Perpendicular to the line y = A) y = - 7x - 17

1 x + 2; containing the point (3, -4) 7 B) y = 7x - 17

C) y = -

1 17 x7 7

D) y = - 7x + 17

Objective: (1.3) Find Equations of Perpendicular Lines

203) Perpendicular to the line 4x - y = 4; containing the point (0, 1) 1 1 1 A) y = x + 1 B) y = - x + 4 C) y = - x + 1 4 4 4

D) y =

3 4

Objective: (1.3) Find Equations of Perpendicular Lines

204) Perpendicular to the line x - 4y = 7; containing the point (4, 4) A) y = - 4x + 20

B) y = - 4x - 20

C) y = 4x - 20

D) y = -

C) x = 3

D) y = 9

C) x = 1

D) x = 4

Objective: (1.3) Find Equations of Perpendicular Lines

205) Perpendicular to the line y = -2; containing the point (9, 3) A) y = 3 B) x = 9 Objective: (1.3) Find Equations of Perpendicular Lines

206) Perpendicular to the line x = -5; containing the point (4, 1) A) y = 1 B) y = 4 Objective: (1.3) Find Equations of Perpendicular Lines

1 x-5 4

207) Perpendicular to the line -4x + 3y = -1; containing the point (7, -9) A) -3x + 4y = 15 B) -3x - 4y = 15 C) 7x - 3y = -1

D) -4x - 3 = -4

Objective: (1.3) Find Equations of Perpendicular Lines

208) Perpendicular to the line -7x + 8y = 41; containing the point (1, 0) A) 8x - 7y = 8 B) -7x - 8y = 8 C) 8x + 7y = 8

D) 8x - 7y = 41

Objective: (1.3) Find Equations of Perpendicular Lines

209) Perpendicular to the line -3x - 5y = -6; y-intercept = 3 A) -3x - 5y = -9 B) -5x + 3y = -15

C) -5x + 3y = 9

D) -3x - 5y = -15

Objective: (1.3) Find Equations of Perpendicular Lines

Decide whether the pair of lines is parallel, perpendicular, or neither. 210) 3x - 4y = -10 8x + 6y = 3 A) parallel B) perpendicular

C) neither

Objective: (1.3) Find Equations of Perpendicular Lines

211) 3x - 6y = 9 18x + 9y = 13 A) parallel

B) perpendicular

C) neither

Objective: (1.3) Find Equations of Perpendicular Lines

212) 6x + 2y = 8 9x + 3y = 14 A) parallel

B) perpendicular

C) neither

Objective: (1.3) Find Equations of Perpendicular Lines

Write the standard form of the equation of the circle. 213) y

(4, 4)

(8, 4)

A) (x + 6)2 + (y + 4)2 = 2 C) (x - 6)2 + (y - 4)2 = 2

B) (x + 6)2 + (y + 4)2 = 4 D) (x - 6)2 + (y - 4)2 = 4

Objective: (1.4) Write the Standard Form of the Equation of a Circle

214) y 10

-10

-5

-10

A) (x - 1)2 + (y - 4)2 = 16 C) (x + 4)2 + (y + 1)2 = 16

B) (x - 4)2 + (y - 1)2 = 16 D) (x + 1)2 + (y + 4)2 = 16

Objective: (1.4) Write the Standard Form of the Equation of a Circle

Write the standard form of the equation of the circle with radius r and center (h, k). 215) r = 3; (h, k) = (0, 0) A) (x - 3)2 + (y - 3)2 = 3 B) (x - 3)2 + (y - 3)2 = 9 C) x2 + y2 = 3

D) x2 + y2 = 9

Objective: (1.4) Write the Standard Form of the Equation of a Circle

216) r = 12; (h, k) = (8, 5) A) (x - 8)2 + (y - 5)2 = 12

B) (x + 8)2 + (y + 5)2 = 12 D) (x - 8)2 + (y - 5)2 = 144

C) (x + 8)2 + (y + 5)2 = 144

Objective: (1.4) Write the Standard Form of the Equation of a Circle

217) r = 8; (h, k) = (-7, 0) A) x2 + (y + 7)2 = 8

B) (x + 7)2 + y2 = 64

C) (x - 7)2 + y2 = 64

D) x2 + (y - 7)2 = 8

Objective: (1.4) Write the Standard Form of the Equation of a Circle

218) r = 10; (h, k) = (0, -3) A) (x - 3)2 + y2 = 100

B) x2 + (y - 3)2 = 10

C) (x + 3)2 + y2 = 100

D) x2 + (y + 3)2 = 100

Objective: (1.4) Write the Standard Form of the Equation of a Circle

219) r =

7; (h, k) = (-1, -4)

A) (x + 4)2 + (y + 1)2 = 49 C) (x - 4)2 + (y - 1)2 = 49

B) (x - 1)2 + (y - 4)2 = 7 D) (x + 1)2 + (y + 4)2 = 7

Objective: (1.4) Write the Standard Form of the Equation of a Circle

220) r =

13; (h, k) = (0, 8) A) (x + 8)2 + y2 = 169

B) x2 + (y - 8)2 = 13

C) x2 + (y + 8)2 = 13

Objective: (1.4) Write the Standard Form of the Equation of a Circle

D) (x - 8)2 + y2 = 169

Solve the problem. 221) Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. A) (x - 1)2 + (y - 1)2 = 136 B) (x - 1)2 + (y - 1)2 = 34 C) (x + 1)2 + (y + 1)2 = 34

D) (x + 1)2 + (y + 1)2 = 136

Objective: (1.4) Write the Standard Form of the Equation of a Circle

222) Find the equation of a circle in standard form with center at the point (-3, 2) and tangent to the line y = 4. A) (x + 3)2 + (y - 2)2 = 16 B) (x - 3)2 + (y + 2)2 = 4 C) (x - 3)2 + (y + 2)2 = 16

D) (x + 3)2 + (y - 2)2 = 4

Objective: (1.4) Write the Standard Form of the Equation of a Circle

223) Find the equation of a circle in standard form that is tangent to the line x = -3 at (-3, 5) and also tangent to the line x = 9. A) (x + 3)2 + (y - 5)2 = 36 B) (x - 3)2 + (y + 5)2 = 36 C) (x - 3)2 + (y - 5)2 = 36

D) (x + 3)2 + (y + 5)2 = 36

Objective: (1.4) Write the Standard Form of the Equation of a Circle

Find the center (h, k) and radius r of the circle with the given equation. 224) x2 + y2 = 4 A) (h, k) = (0, 0); r = 4

B) (h, k) = (2, 2); r = 4

C) (h, k) = (0, 0); r = 2

Objective: (1.4) Write the Standard Form of the Equation of a Circle

225) (x + 2)2 + (y + 6)2 = 49 A) (h, k) = (-2, -6); r = 49 C) (h, k) = (-2, -6); r = 7

B) (h, k) = (-6, -2); r = 7 D) (h, k) = (-6, -2); r = 49

Objective: (1.4) Write the Standard Form of the Equation of a Circle

226) (x + 7)2 + y2 = 100 A) (h, k) = (0, -7); r = 100 C) (h, k) = (-7, 0); r = 100

B) (h, k) = (-7, 0); r = 10 D) (h, k) = (0, -7); r = 10

Objective: (1.4) Write the Standard Form of the Equation of a Circle

227) x2 + (y + 6)2 = 36 A) (h, k) = (-6, 0); r = 36 C) (h, k) = (-6, 0); r = 6

B) (h, k) = (0, -6); r = 6 D) (h, k) = (0, -6); r = 36

Objective: (1.4) Write the Standard Form of the Equation of a Circle

228) 3(x + 1)2 + 3(y - 4)2 = 21 A) (h, k) = (1, -4); r = C) (h, k) = (-1, 4); r =

7 7

B) (h, k) = (1, -4); r = 3 7 D) (h, k) = (-1, 4); r = 3 7

Objective: (1.4) Write the Standard Form of the Equation of a Circle

D) (h, k) = (2, 2); r = 2

Solve the problem. 229) Find the standard form of the equation of the circle. Assume that the center has integer coordinates and the radius is an integer.

A) (x - 1)2 + (y + 2)2 = 9 C) x2 + y2 - 2x + 4y - 4 = 0

B) (x + 1)2 + (y - 2)2 = 9 D) x2 + y2 + 2x - 4y - 4 = 0

Objective: (1.4) Write the Standard Form of the Equation of a Circle

Graph the circle with radius r and center (h, k). 230) r = 4; (h, k) = (0, 0) y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

231) r = 2; (h, k) = (0, 2) y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

232) r = 4; (h, k) = (4, 0) y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

233) r = 4; (h, k) = (4, 1) y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

Graph the equation. 234) x2 + y2 = 16 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

235) (x + 3)2 + (y - 5)2 = 9 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

236) x2 + (y - 6)2 = 4 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

237) (x - 3)2 + y2 = 4 y 10

-10

-5

-10

B) y

-10

-5

-10

-5

-10

D) y

-10

-5

-10

-5

-10

Objective: (1.4) Graph a Circle

Find the center (h, k) and radius r of the circle. Graph the circle. 238) x2 + y2 - 2x - 4y - 4 = 0 y 10

-10

-5

-10

A) (h, k) = (-1, 2); r = 3

B) (h, k) = (-1, -2); r = 3

-10

-5

-10

-5

-10

C) (h, k) = (1, -2); r = 3

D) (h, k) = (1, 2); r = 3

-10

-5

-10

-5

-10

Objective: (1.4) Work with the General Form of the Equation of a Circle

239) x2 + y2 + 2x + 10y + 17 = 0 y 10

-10

-5

-10

A) (h, k) = (-1, 5); r = 3

B) (h, k) = (1, -5); r = 3

-10

-5

-10

-5

-10

C) (h, k) = (1, 5); r = 3

D) (h, k) = (-1, -5); r = 3

-10

-5

-10

-5

-10

Objective: (1.4) Work with the General Form of the Equation of a Circle

Find the center (h, k) and radius r of the circle with the given equation. 240) x2 + 6x + 9 + (y + 7)2 = 25 A) (h, k) = (3, 7); r = 25 B) (h, k) = (-3, -7); r = 5 C) (h, k) = (-7, -3); r = 5 D) (h, k) = (7, 3); r = 25 Objective: (1.4) Work with the General Form of the Equation of a Circle

241) x2 - 8x + 16 + y2 - 16y + 64 = 4 A) (h, k) = (4, 8); r = 2 C) (h, k) = (8, 4); r = 2

B) (h, k) = (-4, -8); r = 4 D) (h, k) = (-8, -4); r = 4

Objective: (1.4) Work with the General Form of the Equation of a Circle

242) x2 + y2 - 8x - 12y + 52 = 25 A) (h, k) = (6, 4); r = 5 C) (h, k) = (-4, -6); r = 25

B) (h, k) = (4, 6); r = 5 D) (h, k) = (-6, -4); r = 25

Objective: (1.4) Work with the General Form of the Equation of a Circle

243) x2 + y2 - 2x - 8y = 8 A) (h, k) = (-1, -4); r = 25 C) (h, k) = (4, 1); r = 5

B) (h, k) = (-4, -1); r = 25 D) (h, k) = (1, 4); r = 5

Objective: (1.4) Work with the General Form of the Equation of a Circle

244) 4x2 + 4y2 - 12x + 16y - 5 = 0 3 30 A) (h, k) = ( , -2); r = 2 2 C) (h, k) = (-

3 , 2); r = 2

B) (h, k) = (-

30 2

3 3 5 , 2); r= 2 2

3 3 5 D) (h, k) = ( , -2); r = 2 2

Objective: (1.4) Work with the General Form of the Equation of a Circle

Find the general form of the equation of the the circle. 245) Center at the point (-4, -3); containing the point (-3, 3) A) x2 + y2 + 6x - 6y - 17 = 0 C) x2 + y2 - 6x + 6y - 12 = 0

B) x2 + y2 + 6x + 8y - 17 = 0 D) x2 + y2 + 8x + 6y - 12 = 0

Objective: (1.4) Work with the General Form of the Equation of a Circle

246) Center at the point (2, -3); containing the point (5, -3) A) x2 + y2 - 4x + 6y + 4 = 0 C) x2 + y2 + 4x - 6y + 22 = 0

B) x2 + y2 - 4x + 6y + 22 = 0 D) x2 + y2 + 4x - 6y + 4 = 0

Objective: (1.4) Work with the General Form of the Equation of a Circle

247) Center at the point (-5, -3); tangent to y-axis A) x2 + y2 + 10x + 6y + 9 = 0

B) x2 + y2 + 10x + 6y + 59 = 0 D) x2 + y2 + 10x + 6y + 25 = 0

C) x2 + y2 - 10x - 6y + 9 = 0

Objective: (1.4) Work with the General Form of the Equation of a Circle

Solve the problem. 248) If a circle of radius 5 is made to roll along the x-axis, what is the equation for the path of the center of the circle? A) y = 10 B) x = 5 C) y = 5 D) y = 0 Objective: (1.4) Work with the General Form of the Equation of a Circle

249) Earth is represented on a map of the solar system so that its surface is a circle with the equation x2 + y2 + 6x + 4y - 3,956 = 0. A weather satellite circles 0.7 units above the Earth with the center of its circular orbit at the center of the Earth. Find the general form of the equation for the orbit of the satellite on this map. A) x2 + y2 - 6x - 4y - 4,044.69 = 0 B) x2 + y2 + 6x + 4y - 4,044.69 = 0 C) x2 + y2 + 6x + 4y - 49.51 = 0

D) x2 + y2 + 6x + 4y + 12.51 = 0

Objective: (1.4) Work with the General Form of the Equation of a Circle

250) Find an equation of the line containing the centers of the two circles x2 + y2 - 2x - 6y + 9 = 0 and x2 + y2 - 12x - 10y + 57 = 0 A) 2x + 5y - 13 = 0 B) -2x + 5y - 13 = 0

C) 8x - 7y - 13 = 0

D) -2x - 5y - 13 = 0

Objective: (1.4) Work with the General Form of the Equation of a Circle

251) A wildlife researcher is monitoring a black bear that has a radio telemetry collar with a transmitting range of 24 miles. The researcher is in a research station with her receiver and tracking the bear's movements. If we put the origin of a coordinate system at the research station, what is the equation of all possible locations of the bear where the transmitter would be at its maximum range? A) x2 + y2 = 48 B) x2 + y2 = 24 C) x2 + y2 = 576 D) x2 - y2 = 24 Objective: (1.4) Work with the General Form of the Equation of a Circle

252) If a satellite is placed in a circular orbit of 240 kilometers above the Earth, what is the equation of the path of the satellite if the origin is placed at the center of the Earth (the diameter of the Earth is approximately 12,740 kilometers)? A) x2 + y2 = 168,480,400 B) x2 + y2 = 57,600 C) x2 + y2 = 40,576,900

D) x2 + y2 = 43,692,100

Objective: (1.4) Work with the General Form of the Equation of a Circle

253) A power outage affected all homes and businesses within a 10 mi radius of the power station. If the power station is located 10 mi north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage. A) x2 + (y + 10)2 = 100 B) x2 + y2 = 100 C) x2 + (y - 10)2 = 10 D) x2 + (y - 10)2 = 100 Objective: (1.4) Work with the General Form of the Equation of a Circle

254) A power outage affected all homes and businesses within a 3 mi radius of the power station. If the power station is located 4 mi west and 3 mi north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage. A) (x - 4)2 + (y + 3)2 = 9 B) (x + 4)2 + (y + 3)2 = 9 C) (x + 4)2 + (y - 3)2 = 9

D) (x - 4)2 + (y - 3)2 = 9

Objective: (1.4) Work with the General Form of the Equation of a Circle

255) A Ferris wheel has a diameter of 320 feet and the bottom of the Ferris wheel is 12 feet above the ground. Find the equation of the wheel if the origin is placed on the ground directly below the center of the wheel, as illustrated.

320 ft.

12 ft.

A) x2 + (y - 160)2 = 25,600 C) x2 + (y - 172)2 = 25,600

B) x2 + y2 = 25,600 D) x2 + (y - 160)2 = 102,400

Objective: (1.4) Work with the General Form of the Equation of a Circle

Answer Key Testname: UNTITLED1

1) A 2) B 3) C 4) D 5) A 6) C 7) D 8) C 9) A 10) C 11) D 12) D 13) D 14) B 15) C 16) C 17) B 18) B 19) B 20) B 21) D 22) B 23) C 24) B 25) A 26) D 27) C 28) B 29) A 30) A 31) A 32) A 33) B 34) B 35) B 36) A 37) D 38) C 39) A 40) C 41) D 42) A 43) D 44) A 45) D 46) B 47) D 48) C 49) D 50) C 79

Answer Key Testname: UNTITLED1

51) B 52) D 53) B 54) B 55) D 56) B 57) C 58) C 59) D 60) D 61) B 62) B 63) A 64) B 65) C 66) B 67) D 68) A 69) C 70) C 71) D 72) C 73) B 74) D 75) B 76) C 77) D 78) C 79) D 80) D 81) D 82) D 83) A 84) A 85) C 86) B 87) A 88) D 89) B 90) A 91) B 92) B 93) A 94) B 95) A 96) C 97) E 98) B 99) A 100) A 80

Answer Key Testname: UNTITLED1

101) D 102) D 103) E 104) C 105) A 106) C 107) E 108) C 109) E 110) B 111) B 112) D 113) B 114) B 115) B 116) C 117) B 118) C 119) A 120) B 121) B 122) B 123) D 124) D 125) B 126) D 127) B 128) A 129) C 130) D 131) C 132) D 133) D 134) A 135) B 136) A 137) C 138) A 139) B 140) A 141) C 142) B 143) D 144) B 145) C 146) C 147) B 148) D 149) A 150) D 81

Answer Key Testname: UNTITLED1

151) C 152) A 153) D 154) D 155) D 156) D 157) A 158) D 159) C 160) A 161) B 162) A 163) C 164) A 165) C 166) A 167) B 168) A 169) A 170) D 171) D 172) D 173) B 174) A 175) D 176) C 177) A 178) B 179) A 180) C 181) B 182) A 183) C 184) A 185) B 186) C 187) C 188) B 189) D 190) D 191) D 192) A 193) A 194) B 195) A 196) D 197) B 198) C 199) D 200) D 82

Answer Key Testname: UNTITLED1

201) A 202) D 203) C 204) A 205) B 206) A 207) B 208) C 209) C 210) B 211) B 212) A 213) D 214) B 215) D 216) D 217) B 218) D 219) D 220) B 221) B 222) D 223) C 224) C 225) C 226) B 227) B 228) C 229) B 230) C 231) B 232) A 233) B 234) D 235) C 236) C 237) D 238) D 239) D 240) B 241) A 242) B 243) D 244) A 245) D 246) A 247) A 248) C 249) B 250) B 83

Answer Key Testname: UNTITLED1

251) C 252) D 253) D 254) C 255) C

Sullivan Trigonometry: A Unit Circle Approach 12e Chapter 2 Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the relation represents a function. If it is a function, state the domain and range. 1) 5 → 15 9 → 27 13 → 39 17 → 51 A) function domain: {5, 9, 13, 17} range: {15, 27, 39, 51}

B) function domain:{15, 27, 39, 51} range: {5, 9, 13, 17}

C) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

2) Alice Brad Carl

snake cat dog

A) function domain: {snake, cat, dog} range: {Alice, Brad, Carl}

B) function domain: {Alice, Brad, Carl} range: {snake, cat, dog}

C) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

3) Alice Brad Carl

cat dog

A) function domain: {cat, dog} range: {Alice, Brad, Carl}

B) function domain: {Alice, Brad, Carl} range: {cat, dog}

C) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

4) {(-3, -6), (2, 4), (4, -4), (8, -2)} A) function domain: {-3, 2, 4, 8} range: {-6, 4, -4, -2}

B) function domain: {-6, 4, -4, -2} range: {-3, 2, 4, 8}

C) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

5) {(5, -3), (-4, -2), (-4, 0), (0, 2), (12, 4)} A) function domain: {-3, -2, 0, 2, 4} range: {5, 0, -4, 12}

B) function domain: {5, 0, -4, 12} range: {-3, -2, 0, 2, 4}

Objective: (2.1) Determine Whether a Relation Represents a Function

C) not a function

6) {(-3, 6), (-2, 1), (0, -3), (2, 1), (4, 13)} A) function domain: {-3, -2, 0, 2, 4} range: {6, 1, -3, 13}

B) function domain: {6, 1, -3, 13} range: {-3, -2, 0, 2, 4}

C) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

5 7) {(9.33, 10.93), (9.333, -10.9), ( , 0), (0.71, -9)} 7 A) function

5 domain: {9.33, 9.333, , 0.71} 7 range: {10.93, -10.9, 0, -9}

B) function domain: {10.93, -10.9, 0, -9} 5 range: {9.33, 9.333, , 0.71} 7

Objective: (2.1) Determine Whether a Relation Represents a Function

Determine whether the equation defines y as a function of x. 8) y = x 3 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

9) y =

1 x

A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

10) y = |x| A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

11) y2 = 6 - x 2 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

12) y = ± 1 - 6x A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

13) x = y2 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

14) y2 + x = 4 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

15) y = 2x2 - 4x + 3 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

C) not a function

16) y =

4x + 1 x-2

A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

17) x2 + 3y2 = 1 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

18) x + 7y = 4 A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

19) -2x + x2 + 24 = y A) function

B) not a function

Objective: (2.1) Determine Whether a Relation Represents a Function

Find the value for the function.

20) Find f(-1) when f(x) = x 2 - 3x + 5. A) 3 B) -1

C) 9

D) -7

C) - 2

D) -

C) 15

D) 3

Objective: (2.1) Find the Value of a Function

21) Find f(-1) when f(x) = A)

x2 - 7 . x-3

3 2

B) - 4

1 4

Objective: (2.1) Find the Value of a Function

22) Find f(-9) when f(x) = |x|- 6. A) -3

B) -15

Objective: (2.1) Find the Value of a Function

23) Find f(2) when f(x) = A) 14

x2 + 5x. B)

Objective: (2.1) Find the Value of a Function

24) Find f(-x) when f(x) = 2x2 - 5x - 4. A) -2x2 + 5x + 4 B) 2x2 + 5x + 4

C) -2x2 + 5x - 4

D) 2x2 + 5x - 4

Objective: (2.1) Find the Value of a Function

25) Find f(-x) when f(x) = A)

-x 2 x +2

x . x2 + 2 B)

x 2 -x + 2

Objective: (2.1) Find the Value of a Function

-x -x2 + 2

-x 2 x -2

26) Find -f(x) when f(x) = 3x2 - 2x + 1. A) -3x2 + 2x + 1 B) 3x2 + 2x + 1

C) -3x2 + 2x - 1

D) 3x2 + 2x - 1

C) -|x| + 7

D) -|x| - 7

C) 4x2 - 13x - 7

D) -13x2 + 4x + 3

Objective: (2.1) Find the Value of a Function

27) Find -f(x) when f(x) = |x| - 7. A) |-x| - 7

B) |-x| + 7

Objective: (2.1) Find the Value of a Function

28) Find f(x - 1) when f(x) = 4x 2 - 5x - 6. A) 4x2 - 13x + 3 B) 4x2 - 29x - 7 Objective: (2.1) Find the Value of a Function

29) Find f(x + 1) when f(x) = A)

x2 + 2x + 9 x+5

x2 - 8 . x+4 B)

x2 + 2x - 7 x+5

x2 + 2x - 7 x-3

x2 - 7 x+5

Objective: (2.1) Find the Value of a Function

30) Find f(2x) when f(x) = 3x2 + 4x + 5. A) 12x2 + 8x + 10 B) 6x2 + 8x + 5

C) 12x2 + 8x + 5

D) 6x2 + 8x + 10

C) 2 6x2 - 5x

Objective: (2.1) Find the Value of a Function

31) Find f(2x) when f(x) = A) 24x2 - 10x

6x2 - 5x. 12x2 - 20x

12x2 - 10x

Objective: (2.1) Find the Value of a Function

32) Find f(x + h) when f(x) = 3x2 + 2x + 2. A) 3x2 + 3h 2 + 2x + 2h + 2

B) 3x2 + 3h 2 + 8x + 8h + 2 D) 3x2 + 6xh + 3h 2 + 2x + 2h + 2

C) 3x2 + 3xh + 3h 2 + 2x + 2h + 2

Objective: (2.1) Find the Value of a Function

33) Find f(x + h) when f(x) = A)

-8x + 3h 3x - 7h

-8x + 3 . 3x - 7 B)

-8x - 8h + 3 3x + 3h - 7

-8x - 5h 3x - 4h

-8x - 8h + 3 3x - 7

Objective: (2.1) Find the Value of a Function

Solve the problem.

34) If f(x) = 8x 3 + 8x2 - x + C and f(2) = 1, what is the value of C? A) C = 35 B) C = 99 C) C = -1 Objective: (2.1) Find the Value of a Function

D) C = -93

35) If f(x) =

x-B , f(-1) = 0, and f(-7) is undefined, what are the values of A and B? x-A

A) A = -1, B = -7

B) A = 7, B = 1

C) A = 1, B = 7

D) A = -7, B = -1

C) A = 25

D) A = -77

Objective: (2.1) Find the Value of a Function

36) If f(x) =

x - 5A and f(5) = 15, what is the value of A? 5x + 1

A) A = -25

B) A = 77

Objective: (2.1) Find the Value of a Function

37) If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 80 - 4.9x2 . What is the height of the rock when x = 1.6 seconds? Round to the nearest hundredth, if necessary. A) 92.54 m B) 72.16 m C) 67.71 m D) 67.46 m Objective: (2.1) Find the Value of a Function

38) If a rock falls from a height of 40 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 40 - 4.9x2 . When does the rock strike the ground? Round to the nearest hundredth, if necessary. A) 8.16 sec B) 1.29 sec C) 1.67 sec

D) 2.86 sec

Objective: (2.1) Find the Value of a Function

39) It has been determined that the number of fish f(t) that can be caught in t minutes in a certain pond using a certain bait is f(t) = 0.21t + 1, for t > 10. Find the approximate number of fish that can be caught if you fish for 28 minutes. A) About 6 fish B) About 30 fish C) About 15 fish D) About 32 fish Objective: (2.1) Find the Value of a Function

40) The function P(d) = 1 + at 41 feet. 8 A) atm 33

d gives the pressure, in atmospheres (atm), at a depth d feet in the sea. Find the pressure 33 B)

41 atm 33

74 atm 33

14 atm 11

Objective: (2.1) Find the Value of a Function

41) The function F described by F(C) =

9 C + 32 gives the Fahrenheit temperature corresponding to the Celsius 5

temperature C. Find the Fahrenheit temperature equivalent to 25°C. A) 122°F B) 167°F C) 77°F

D) 212°F

Objective: (2.1) Find the Value of a Function

Find the domain of the function. 42) f(x) = 2x + 2 A) all real numbers

B) {x|x ≥ -2}

C) {x|x > 0}

D) {x|x ≠ 0}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

43) f(x) = x2 + 6 A) all real numbers

B) {x|x > -6}

C) {x|x ≥ -6}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

D) {x|x ≠ -6}

44) f(x) =

x2 x2 + 19

A) {x|x > -19}

B) {x|x ≠ -19}

C) all real numbers

D) {x|x ≠ 0}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

45) g(x) =

3x 2 x -9

A) all real numbers

B) {x|x ≠ 0}

C) {x|x ≠ -3, 3}

D) {x|x > 9}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

46) h(x) =

x-2 x3 - 81x

A) {x|x ≠ 0}

B) {x|x ≠ 2}

C) all real numbers

D) {x|x ≠ -9, 0, 9}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

47) f(x) = 5 - x A) {x|x ≠ 5}

B) {x|x ≤

C) {x|x ≤ 5}

D) {x|x ≠

Objective: (2.1) Find the Domain of a Function Defined by an Equation

48)

x x-7 A) {x|x ≥ 7}

B) {x|x ≠ 7}

C) all real numbers

D) {x|x > 7}

Objective: (2.1) Find the Domain of a Function Defined by an Equation

For the given functions f and g, find the requested function and state its domain. 49) f(x) = 5 - 3x; g(x) = -7x + 3 Find f + g. A) (f + g)(x) = 4x + 8; {x|x ≠ 2}

B) (f + g)(x) = -2x; all real numbers

C) (f + g)(x) = -10x + 8; all real numbers

D) (f + g)(x) = -7x + 5; {x| x ≠

5 } 7

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

50) f(x) = 3x - 4; g(x) = 8x - 3 Find f - g. A) (f - g)(x) = -5x - 7; {x|x ≠ -

7 } 5

B) (f - g)(x) = 5x + 1; all real numbers

C) (f - g)(x) = 11x - 7; {x|x ≠ 1}

D) (f - g)(x) = -5x - 1; all real numbers

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

51) f(x) = 4x - 8; g(x) = 9x + 3 Find f ∙ g. A) (f ∙ g)(x) = 36x2 - 69x - 24; {x|x ≠ -24}

B) (f ∙ g)(x) = 36x2 - 24; {x|x ≠ -24} D) (f ∙ g)(x) = 13x2 - 60x - 5; all real numbers

C) (f ∙ g)(x) = 36x2 - 60x - 24; all real numbers

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

52) f(x) = 6x + 5; g(x) = 4x - 3 f Find . g A)

f 4x - 3 (x) = ; g 6x + 5

x|x ≠ -

f 6x + 5 (x) = ; g 4x - 3

x|x ≠

5 6

3 4

f 4x - 3 (x) = ; g 6x + 5

x|x ≠

3 4

f 6x + 5 (x) = ; g 4x - 3

x|x ≠ -

5 6

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

53) f(x) = 16 - x 2 ; g(x) = 4 - x Find f + g.

B) (f + g)(x) = -x2 + x + 12; all real numbers D) (f + g)(x) = x 3 - 4x2 - 16x + 64; all real numbers

A) (f + g)(x) = 4 + x; {x|x ≠ -4} C) (f + g)(x) = -x2 - x + 20; all real numbers

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

54) f(x) = x + 9; g(x) = 7x 2 Find f + g. A) (f + g)(x) = 7x2 + x + 9; {x|x ≠ -9}

B) (f + g)(x) = -7x2 + x + 9; all real numbers D) (f + g)(x) = 7x2 + x + 9; all real numbers

C) (f + g)(x) = 7x 2 - x - 9; all real numbers

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

55) f(x) = 5x 3 + 2; g(x) = 5x2 - 3 Find f ∙ g. A) (f ∙ g)(x) = 25x5 - 15x3 + 10x2 - 6; {x|x ≠ 0}

B) (f ∙ g)(x) = 5x 3 + 5x2 - 6; all real numbers C) (f ∙ g)(x) = 25x5 - 15x3 + 10x2 - 6; all real numbers

D) (f ∙ g)(x) = 25x6 - 15x3 + 10x2 - 6; all real numbers Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

56) f(x) =

f Find . g

x; g(x) = 4x - 9

f x (x) = ; g 4x - 9

f 4x - 9 (x) = ; {x|x ≥ 0} g x

x|x ≥ 0, x ≠

9 4

f x (x) = ; {x|x ≠ 0} g 4x - 9

f x (x) = ; g 4x - 9

x|x ≠

9 4

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

57) f(x) = 5 - x; g(x) = Find f ∙ g.

x-2

A) (f ∙ g)(x) =

-x2 - 10; {x|x ≠ 10}

B) (f ∙ g)(x) =

(5 - x)(x - 2); {x|x ≠ 2, x ≠ 5}

C) (f ∙ g)(x) =

(5 - x)(x - 2); {x|x ≥ 0}

D) (f ∙ g)(x) =

(5 - x)(x - 2); {x|2 ≤ x ≤ 5}

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

58) f(x) =

7x + 8 5x ; g(x) = 3x - 5 3x - 5

Find f - g. A) (f - g)(x) =

12x - 8 ; 3x - 5

5 3

C) (f - g)(x) =

2x + 8 ; {x|x ≠ 0} 3x - 5

x|x ≠

B) (f - g)(x) =

2x + 8 ; 3x - 5

x|x ≠

5 ,x≠- 4 3

D) (f - g)(x) =

2x + 8 ; 3x - 5

x|x ≠

5 3

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

59) f(x) =

x + 5; g(x) =

2 x

Find f ∙ g. A) (f ∙ g)(x) =

2 x+5 ; {x|x ≥ -5, x ≠ 0} x

B) (f ∙ g)(x) =

7 ; {x|x ≠ 0} x

C) (f ∙ g)(x) =

2x + 10 ; {x|x ≥ -5, x ≠ 0} x

D) (f ∙ g)(x) =

2x + 10 ; {x|x ≥ -5, x ≠ 0} x

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

Solve the problem. 60) Given f(x) = A) g(x) =

1 f x+3 and ( )(x) = , find the function g. x g x2 + 7x x-7 x-3

B) g(x) =

x-3 x-7

C) g(x) =

x+7 x+3

D) g(x) =

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

61) Find (f + g)(2) when f(x) = x + 1 and g(x) = x + 6. A) -3 B) -1

C) 11

D) 9

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

62) Find (f - g)(1) when f(x) = -5x2 - 4 and g(x) = x + 3. A) -11 B) -7

C) -13

D) 8

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

63) Find (fg)(-3) when f(x) = x + 2 and g(x) = 2x2 + 17x + 7. A) 130 B) 26

C) 35

D) -125

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

64) Find

f (-5) when f(x) = 5x - 2 and g(x) = 2x 2 + 14x + 5. g

A) -

2 15

2 23

9 5

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

D) 0

x+3 x+7

Find and simplify the difference quotient of f,

f(x + h) - f(x) , h≠ 0, for the function. h

65) f(x) = 5x - 2 A) 0

B) 5 +

-4 h

C) 5 +

10(x - 2) h

D) 5

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

66) f(x) = 4x 2 A) 4(2x+h)

B) 4

8 + x + 4h h

4(2x2 + 2xh + h 2 ) h

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

67) f(x) = 5 A) 1 +

10 h

B) 5

C) 1

D) 0

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

68) f(x) = A)

1 6x -1 x(x + h)

B) 0

-1 6x (x + h)

1 6x

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

69) f(x) = x2 + 3x + 5

2x2 + 2x + 2xh + h 2 + h + 10 h

A) 2x+ h + 5

C) 2x+ h + 3

D) 1

Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

Solve the problem. 70) Express the gross salary G of a person who earns $20 per hour as a function of the number x of hours worked. 20 A) G(x) = 20 + x B) G(x) = C) G(x) = 20x2 D) G(x) = 20x x Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

71) Jacey, a commissioned salesperson, earns $440 base pay plus $45 per item sold. Express Jacey's gross salary G as a function of the number x of items sold. A) G(x) = 45(x + 440) B) G(x) = 45x + 440 C) G(x) = 440x +45 D) G(x) = 440(x + 45) Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

72) Suppose that P(x) represents the percentage of income spent on automobile insurance in year x and I(x) represents income in year x. Determine a function A that represents total automobile insurance expenditures in year x. I A) A(x) = (P ∙ I)(x) B) A(x) = (x) C) A(x) = (P + I)(x) D) A(x) = (I - P)(x) P Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

73) A retail store buys 50 VCRs from a distributor at a cost of $235 each plus an overhead charge of $25 per order. The retail markup is 45% on the total price paid. Find the profit on the sale of one VCR. A) $105.53 B) $105.75 C) $10,598.00 D) $105.98 Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

74) The following graph shows the private, public and total national school enrollment for students for select years from 1970 through 2000.

i) How is the graph for total school enrollment, T, determined from the graph of the private enrollment, r, and the public enrollment, u? ii) During which 10-year period did the total number of students enrolled increase the least? iii) During which 10-year period did the total number of students enrolled increase the most? A) i) T is the sum of r and u. B) i) T is the sum of r and u. ii) 1970 - 1980 ii) 1990-2000 iii) 1980-1990 iii) 1970-1980 C) i) T is the difference of r and u. D) i) T is the sum of r and u. ii) 1970 - 1980 ii) 1970 - 1980 iii) 1990-2000 iii) 1990-2000 Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

75) A firm is considering a new product. The accounting department estimates that the total cost, C(x), of producing x units will be C(x) = 75x + 3,990. The sales department estimates that the revenue, R(x), from selling x units will be R(x) = 85x, but that no more than 815 units can be sold at that price. Find and interpret (R - C)(815). A) -$4,160 loss, cost exceeds income B) $4,160 profit, income exceeds cost It is not worth it to develop product. It is worth it to develop product. C) $134,390 profit, income exceeds cost D) $1,214 profit, income exceeds cost It is worth it to develop product. It is worth it to develop product. Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

76) The function f(t) = -0.15t2 + 0.53t + 31.2 models the U.S. population in millions, ages 65 and older, where t represents years after 1990. The function g(t) = 0.53t2 + 12.37t + 107.8 models the total yearly cost of Medicare in billions of dollars, where t represents years after 1990. What does the function

g g represent? Find (5). f f

A) Cost per person in thousands of dollars. $0.16 thousand B) Cost per person in thousands of dollars. $0.21 thousand C) Cost per person in thousands of dollars. $6.08 thousand D) Cost per person in thousands of dollars. $11.73 thousand Objective: (2.1) Form the Sum, Difference, Product, and Quotient of Two Functions

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. 77) y 10

-10

-5

-10

A) function domain: {x|-3 ≤ x ≤ 3} range: all real numbers intercepts: (-3, 0), (3, 0) symmetry: x-axis, y-axis C) function domain: all real numbers range: {y|y ≤ -3 or y ≥ 3} intercepts: (-3, 0), (3, 0) symmetry: y-axis

B) function domain: {x|x ≤ -3 or x ≥ 3} range: all real numbers intercepts: (-3, 0), (3, 0) symmetry: x-axis, y-axis, origin D) not a function

Objective: (2.2) Identify the Graph of a Function

78) y 5

-5

A) function domain: all real numbers range: {y|y > 0} intercept: (1, 0) symmetry: none C) function domain: {x|x > 0} range: all real numbers intercept: (1, 0) symmetry: none

B) function domain: {x|x > 0} range: all real numbers intercept: (0, 1) symmetry: origin D) not a function

Objective: (2.2) Identify the Graph of a Function

79) y 1

-

-3 - 4 2

 4

- 4

 2

3 4



-1

A) function domain: all real numbers range: {y|-1 ≤ y ≤ 1} intercepts: (-π, 0), (0, 0), (π, 0) symmetry: origin C) function domain: {x|-1 ≤ x ≤ 1} range: {y|-π ≤ y ≤ π} intercepts: (-π, 0), (0, 0), (π, 0) symmetry: none

B) function domain: {x|-π ≤ x ≤ π} range: {y|-1 ≤ y ≤ 1} intercepts: (-π, 0), (0, 0), (π, 0) symmetry: origin D) not a function

Objective: (2.2) Identify the Graph of a Function

80) y 10

-10

-5

-10

A) function domain: {x|x ≤ 9} range: all real numbers intercepts: (-2, 0), (0, 8), (4, 0) symmetry: y-axis C) function domain: all real numbers range: {y|y ≤ 9} intercepts: (-2, 0), (0, 8), (4, 0) symmetry: none

B) function domain: all real numbers range: {y|y ≤ 9} intercepts: (0, -2), (8, 0), (0, 4) symmetry: none D) not a function

Objective: (2.2) Identify the Graph of a Function

81) y 10

-10

-5

-10

A) function domain: {x|-5 ≤ x ≤ 5} range: {y|-5 ≤ y ≤ 5} intercepts: (-5, 0), (0, -5), (0, 5), (5, 0) symmetry: x-axis, y-axis, origin C) function domain: {x|-5 ≤ x ≤ 5} range: {y|-5 ≤ y ≤ 5} intercepts: (-5, 0), (0, -5), (0, 5), (5, 0) symmetry: x-axis, y-axis

B) function domain: {x|-5 ≤ x ≤ 5} range: {y|-5 ≤ y ≤ 5} intercepts: (-5, 0), (0, -5), (0, 0), (0, 5), (5, 0) symmetry: origin D) not a function

Objective: (2.2) Identify the Graph of a Function

82) 5

5 x

-5

A) function domain: all real numbers range: all real numbers intercepts: (-2, 0), (0, 2), (2, 0) symmetry: none C) function domain: {x|x ≥ 0} range: {y|y ≥ -2} intercepts: (-2, 0), (0, 2), (2, 0) symmetry: y-axis

B) function domain: {x|x ≥ -2} range: {y|y ≥ 0} intercepts: (-2, 0), (0, 2), (2, 0) symmetry: none D) not a function

Objective: (2.2) Identify the Graph of a Function

83) 10

-10

-5

-10

A) function domain: all real numbers range: all real numbers intercept: (0, 7) symmetry: none C) function domain: {x|x = 4 or x = 7} range: all real numbers intercept: (7, 0) symmetry: x-axis

B) function domain: all real numbers range: {y|y = 4 or y = 7} intercept: (0, 7) symmetry: none D) not a function

Objective: (2.2) Identify the Graph of a Function

The graph of a function f is given. Use the graph to answer the question. 84) Use the graph of f given below to find f(20). 20

-20

-20 A) 40

B) 24

C) 20

Objective: (2.2) Obtain Information from or about the Graph of a Function

85) Is f(-25) positive or negative?

-25

-25 A) positive

B) negative

Objective: (2.2) Obtain Information from or about the Graph of a Function

D) 0

86) Is f(20) positive or negative? 50

-50

-50 A) positive

B) negative

Objective: (2.2) Obtain Information from or about the Graph of a Function

87) For what numbers x is f(x) = 0? 100

100

-100

-100 A) (-100, -60), (70, 100) C) -60, 70, 100

B) (-60, 70) D) -60

Objective: (2.2) Obtain Information from or about the Graph of a Function

88) For what numbers x is f(x) > 0? 20

-20

-20 A) (-12, ∞)

B) [-20, -12), (14, 20)

C) (- ∞ -12)

Objective: (2.2) Obtain Information from or about the Graph of a Function

89) For what numbers x is f(x) < 0? 100

100

-100

-100 A) (- ∞, -60) C) (-60, ∞)

B) (-60, 70) D) [-100, -60), (70, 100)

Objective: (2.2) Obtain Information from or about the Graph of a Function

D) (-12, 14)

90) What is the domain of f? 25

-25

-25 A) {x|-25 ≤ x ≤ 25}

B) {x|x ≥ 0}

C) all real numbers

D) {x|-20 ≤ x ≤ 27.5}

Objective: (2.2) Obtain Information from or about the Graph of a Function

91) What are the x-intercepts? 25

-25

-25 A) -25, -15, 17.5, 25

B) -15, 17.5, 25

C) -15

Objective: (2.2) Obtain Information from or about the Graph of a Function

D) -15, 17.5

92) What is the y-intercept? 25

-25

-25 A) -15

B) 25

C) -20

D) 17.5

Objective: (2.2) Obtain Information from or about the Graph of a Function

93) How often does the line y = -25 intersect the graph? 25

-25

-25 A) once

B) twice

C) three times

Objective: (2.2) Obtain Information from or about the Graph of a Function

D) does not intersect

94) How often does the line y = 10 intersect the graph? 50

-50

-50 A) once

B) twice

C) three times

D) does not intersect

Objective: (2.2) Obtain Information from or about the Graph of a Function

95) For which of the following values of x does f(x) = -16? 20

-20

-20 A) -16

B) 0

C) 8

D) 12

Objective: (2.2) Obtain Information from or about the Graph of a Function

Answer the question about the given function. 96) Given the function f(x) = -7x2 + 14x - 3, is the point (1, 4) on the graph of f? A) Yes

B) No

Objective: (2.2) Obtain Information from or about the Graph of a Function

97) Given the function f(x) = -4x2 - 8x - 6, is the point (-2, -14) on the graph of f? A) Yes B) No Objective: (2.2) Obtain Information from or about the Graph of a Function

98) Given the function f(x) = -2x2 + 4x - 8, if x = 1, what is f(x)? What point is on the graph of f? A) -6; (1, -6) B) -6; (-6, 1) C) -14; (1, -14) D) -14; (-14, 1) Objective: (2.2) Obtain Information from or about the Graph of a Function

99) Given the function f(x) = 7x2 + 14x - 4, what is the domain of f? A) all real numbers B) {x|x ≥-1} C) {x|x ≥ 1}

D) {x|x ≤ -1}

Objective: (2.2) Obtain Information from or about the Graph of a Function

100) Given the function f(x) = x2 + 6x - 40, list the x-intercepts, if any, of the graph of f. A) (-10, 0), (1, 0) B) (10, 0), (-4, 0) C) (10, 0), (4, 0)

D) (-10, 0), (4, 0)

Objective: (2.2) Obtain Information from or about the Graph of a Function

101) Given the function f(x) = 7x2 - 14x + 5, list the y-intercept, if there is one, of the graph of f. A) 5 B) 19 C) -2 D) 26 Objective: (2.2) Obtain Information from or about the Graph of a Function

102) Given the function f(x) =

x2 - 8 7 , is the point (-1, - ) on the graph of f? x+3 2

A) Yes

B) No

Objective: (2.2) Obtain Information from or about the Graph of a Function

103) Given the function f(x) =

x2 - 2 , is the point (2, - 6) on the graph of f? x-3

A) Yes

B) No

Objective: (2.2) Obtain Information from or about the Graph of a Function

104) Given the function f(x) = A)

1 1 ; ( , -2) 3 3

x2 - 5 , if x = -2, what is f(x)? What point is on the graph of f? x-1 B) - 3; (- 3, -2)

C) - 3; (-2, - 3)

1 1 ; (-2, ) 3 3

Objective: (2.2) Obtain Information from or about the Graph of a Function

105) Given the function f(x) = A) {x|x ≠ - 4}

x2 + 8 , what is the domain of f? x+2 B) {x|x ≠ 8}

C) {x|x ≠ 2}

D) {x|x ≠ -2}

Objective: (2.2) Obtain Information from or about the Graph of a Function

106) Given the function f(x) = A) (8, 0), (-8, 0)

x2 + 8 , list the x-intercepts, if any, of the graph of f. x-7 B) (-2 2, 0)

C) (7, 0)

D) none

Objective: (2.2) Obtain Information from or about the Graph of a Function

107) Given the function f(x) = A) (0, -

7 ) 3

x2 + 7 , list the y-intercept, if there is one, of the graph of f. x-3 B) (0, -7)

C) (0, 3)

Objective: (2.2) Obtain Information from or about the Graph of a Function

D) (-

7 , 0) 3

Solve the problem. 108) If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles above sea level is 4000 2 given approximately by W(h) = m . How much will a man who weighs 165 pounds at sea level weigh 4000 + h on the top of a mountain which is 14,494 feet above sea level? Round to the nearest hundredth of a pound, if necessary. A) 165.23 pounds B) 7.72 pounds C) 165 pounds D) 164.77 pounds Objective: (2.2) Obtain Information from or about the Graph of a Function

Match the function with the graph that best describes the situation. 109) The amount of rainfall as a function of time, if the rain fell more and more softly. A) B) y

D) y

Objective: (2.2) Obtain Information from or about the Graph of a Function

110) The height of an animal as a function of time. A)

D) y

Objective: (2.2) Obtain Information from or about the Graph of a Function

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 111) Michael decides to walk to the mall to do some errands. He leaves home, walks 3 blocks in 9 minutes at a constant speed, and realizes that he forgot his wallet at home. So Michael runs back in 8 minutes. At home, it takes him 2 minutes to find his wallet and close the door. Michael walks 5 blocks in 13 minutes and then decides to jog to the mall. It takes him 6 minutes to get to the mall which is 2 blocks away. Draw a graph of Michael's distance from home (in blocks) as a function of time. y

Objective: (2.2) Obtain Information from or about the Graph of a Function

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 112) A steel can in the shape of a right circular cylinder must be designed to hold 750 cubic centimeters of juice (see 1,500 figure). It can be shown that the total surface area of the can (including the ends) is given by S(r) = 2πr2 + , r where r is the radius of the can in centimeters. Using the TABLE feature of a graphing utility, find the radius that minimizes the surface area (and thus the cost) of the can. Round to the nearest tenth of a centimeter.

A) 6.1 cm

B) 4.1 cm

C) 4.9 cm

D) 0 cm

Objective: (2.2) Obtain Information from or about the Graph of a Function

113) The concentration C (arbitrary units) of a certain drug in a patient's bloodstream can be modeled using t C(t) = , where t is the number of hours since a 500 milligram oral dose was administered. Using 0.408t + 2.449 2 the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round to the nearest tenth of an hour. A) 7.5 hours B) 8.3 hours C) 6.8 hours D) 6 hours Objective: (2.2) Obtain Information from or about the Graph of a Function

The graph of a function is given. Decide whether it is even, odd, or neither. 114) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

115) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

116) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

117) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

118) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

119) y 10 8 6 4 2 -10 -8 -6 -4 -2 -2

8 10 x

-4 -6 -8 -10

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

120) y 5 4 3 2 1 -

- 2

 2

-1 -2



-3 -4 -5

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

121) y 5 4 3 2 1 -

- 2

-1 -2

 2



-3 -4 -5

A) even

B) odd

C) neither

Objective: (2.3) Determine Even and Odd Functions from a Graph

Determine algebraically whether the function is even, odd, or neither. 122) f(x) = 5x 3 A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

123) f(x) = 4x4 - x 2 A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

124) f(x) = -7x2 - 6 A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

125) f(x) = 6x 3 - 9 A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

3 126) f(x) = x A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

127) f(x) = x A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

128)

8x2 + 9 A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

129) f(x) =

1 x2

A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

130) f(x) =

x 2 x +5

A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

131) f(x) =

-x3 9x2 + 4

A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

132) f(x) =

-5x |x|

A) even

B) odd

C) neither

Objective: (2.3) Identify Even and Odd Functions from the Equation

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 133) (- 2, - 1) y 5

-5

A) constant

B) decreasing

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

134) (-

3 , 0) 2 y 5

-5

A) constant

B) decreasing

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

135) (0, 1) y 5

-5

A) constant

B) increasing

C) decreasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

136) (1, 2) y 5

-5

A) constant

B) increasing

C) decreasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

137) (0, 2) y 10

-10

-5

-10

A) decreasing

B) constant

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

138) (-2, 0) y 10

-10

-5

-10

A) decreasing

B) increasing

C) constant

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

139) (1, ∞) y 10

-10

-5

-10

A) increasing

B) constant

C) decreasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

140) (2, ∞) y 10

-10

-5

-10

A) constant

B) decreasing

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

141) (0, 1) 3

2 1

-2

-1

-1 -2 -3

A) decreasing

B) constant

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

142) (4, 3) y 5 (1, 3)

(4, 3)

-5

(-5, -2) (-4, -2)

(6, -2) -5

A) constant

B) decreasing

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

143) (-1, 0) y 5

(-6, 1) (-2.5, 0)

(2, 0)

-5

(5, -3) (-1, -4) -5 (0, -4)

A) constant

B) increasing

C) decreasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

144) (2.2, 5) y 10 (-8, 5)

(2.2, 3.9) (-5, 0)

(4, 0)

-10 (-9.5, 0)

10 x

(0, 0) (-2.5, -3.3)

(5, -2.5)

-10

A) constant

B) decreasing

C) increasing

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

Use the graph to find the intervals on which it is increasing, decreasing, or constant. 145)

A) Increasing on (- ∞, 0); decreasing on (0, ∞) C) Increasing on (- ∞, ∞)

B) Decreasing on (-∞, 0); increasing on (0, ∞) D) Decreasing on (-∞, ∞)

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

146)

A) Increasing on (- ∞, ∞) C) Decreasing on (- ∞, 0); increasing on (0, ∞)

B) Increasing on (-∞, 0); decreasing on (0, ∞) D) Decreasing on (-∞, ∞)

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

147)

A) Decreasing on - π, 0 ; increasing on 0, π B) Increasing on (- ∞, ∞) π π π π C) Decreasing on - π, and , π ; increasing on - , 2 2 2 2 D) Increasing on - π, -

π π π π and , π ; decreasing on - , 2 2 2 2

Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

148)

A) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1); constant on (-2, -1) and (1, 2) B) Decreasing on (-3, -1) and (1, 4); increasing on (-2, 1) C) Decreasing on (-3, -2) and (2, 4); increasing on (-1, 1) D) Increasing on (-3, -2) and (2, 4); decreasing on (-1, 1); constant on (-2, -1) and (1, 2) Objective: (2.3) Use a Graph to Determine Where a Function Is Increasing, Decreasing, or Constant

The graph of a function f is given. Use the graph to answer the question. 149) Find the numbers, if any, at which f has a local maximum. What are the local maxima? 5

4 3 2 1 -5

-4

-3

-2

-1

5 x

-2 -3 -4 -5

A) f has a local maximum at x = -2 and 2; the local maximum is 0 B) f has a local maximum at x = 0; the local maximum is 3 C) f has a local maximum at x = 2; the local maximum is 3 D) f has no local maximum Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

150) Find the numbers, if any, at which f has a local minimum. What are the local minima? 5

4 3 2 1 -5

-4

-3

-2

-1

5 x

-2 -3 -4 -5

A) f has a local minimum at x = -3; the local minimum is 0 B) f has a local minimum at x = 0; the local minimum is 3 C) f has a local minimum at x = -3 and 3; the local minimum is 0 D) f has no local minimum Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

151) Find the numbers, if any, at which f has a local maximum. What are the local maxima? 2

-

 2

- 2



-1

-2

A) f has a local maximum at -π; the local maximum is 1 B) f has a local maximum at x = 0; the local maximum is 1 C) f has a local maximum at x = -π and π; the local maximum is -1 D) f has no local maximum Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

152) Find the numbers, if any, at which f has a local minimum. What are the local minima? 2

-

 2

- 2



-1

-2

A) f has no local minimum B) f has a local minimum at x = -π; the local minimum is -2 C) f has a local minimum at x = 0; the local minimum is -2 D) f has a local minimum at x = -π and π; the local minimum is 2 Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

153) y 10 (-8, 5)

(2.2, 3.9) (-5, 0)

(4, 0)

-10 (-9.5, 0)

10 x

(0, 0) (-2.5, -3.3)

(5, -2.5)

-10

Find the numbers, if any, at which f has a local minimum. What are the local maxima? A) f has a local maximum at x = -2.5 and 5; the local maximum at -2.5 is -3.3; the local maximum at 5 is -2.5 B) f has a local maximum at x = -3.3 and -2.5; the local maximum at -3.3 is -2.5; the local maximum at -2.5 is 5 C) f has a local minimum at x = -2.5 and 5; the local minimum at -2.5 is -3.3; the local minimum at 5 is -2.5 D) f has a local minimum at x = -3.3 and -2.5; the local minimum at -3.3 is -2.5; the local minimum at -2.5 is 5 Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

Solve the problem. 154) The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 4 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 70t + 4. What is the maximum height? Round to the nearest hundredth, if necessary. y

A) 91.5 ft

B) 76.81 ft

C) -54.44 ft

Objective: (2.3) Use a Graph to Locate Local Maxima and Local Minima

D) 80.56 ft

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. 155)

A) Absolute maximum: f(2) = 7; Absolute minimum: f(3) = 0 B) Absolute maximum: f(5) = 6; Absolute minimum: f(2) = 1 C) Absolute maximum: f(7) = 2; Absolute minimum: f(0) = 3 D) Absolute maximum: f(6) = 5; Absolute minimum: f(1) = 2 Objective: (2.3) Use a Graph to Locate the Absolute Maximum and the Absolute Minimum

156)

A) Absolute maximum: f(3) = 6; Absolute minimum: f(5) = 1 B) Absolute maximum: f(7) = 4; Absolute minimum: f(0) = 2 C) Absolute maximum: f(3) = 6; Absolute minimum: f(0) = 2 D) Absolute maximum: f(3) = 6; Absolute minimum: none Objective: (2.3) Use a Graph to Locate the Absolute Maximum and the Absolute Minimum

157)

A) Absolute maximum: none; Absolute minimum: f(1) = 2 B) Absolute maximum: f(-1) = 6; Absolute minimum: f(1) = 2 C) Absolute maximum: none; Absolute minimum: none D) Absolute maximum: f(3) = 5; Absolute minimum: f(1) = 2 Objective: (2.3) Use a Graph to Locate the Absolute Maximum and the Absolute Minimum

158)

A) Absolute maximum: none; Absolute minimum: f(1) = 2 B) Absolute maximum: f(4) = 7; Absolute minimum: none C) Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2 D) Absolute maximum: none; Absolute minimum: none Objective: (2.3) Use a Graph to Locate the Absolute Maximum and the Absolute Minimum

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. 159) f(x) = x3 - 3x + 3, (-2, 2) A) local maximum at (-1, 5) local minimum at (1, 1) increasing on (-1, 1) decreasing on (-2, -1) and (1, 2) C) local maximum at (1, 1) local minimum at (-1, 5) increasing on (-2, -1) decreasing on (-1, 1)

B) local maximum at (-1, 5) local minimum at (1, 1) increasing on (-2, -1) and (1, 2) decreasing on (-1, 1) D) local maximum at (1, 1) local minimum at (-1, 5) increasing on (-2, -1) and (1, 2) decreasing on (-1, 1)

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 160) f(x) = x3 - 4x2 + 6; (-1, 4) Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

161) f(x) = x5 - x 2 ; (-2, 2) Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

162) f(x) = -0.3x3 + 0.2x2 + 4x - 5; (-4, 5) Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

163) f(x) = 0.15x 4 + 0.3x3 - 0.8x2 + 5; (-4, 2) Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. 164) f(x) = x2 + 2x - 3; (-5, 5) A) local minimum at (1, 4) C) local minimum at (-1, -4)

B) local maximum at (1, -4) D) local maximum at (-1, 4)

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

165) f(x) = 2 + 8x - x2; (-5, 5) A) local minimum at (-4, 18) C) local maximum at (-4, 50)

B) local minimum at (4, 50) D) local maximum at (4, 18)

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

166) f(x) = x3 - 3x2 + 1; (-5, 5) A) local minimum at (0, 1) local maximum at (2, -3) C) local maximum at (0, 1) local minimum at (2, -3)

B) local minimum at (2, -3) D) none

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

167) f(x) = x3 - 12x + 2; (-5, 5) A) local maximum at (-2, 18) local minimum at (2, -14)

B) local minimum at (0, 0)

C) local maximum at (-2, 18) local minimum at (0, 0) local minimum at (2, -14)

D) none

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

168) f(x) = x4 - 5x3 + 3x2 + 9x - 3; (-5, 5) A) local minimum at (-0.57, -6.12) local maximum at (1.32, 5.64) local minimum at (3, -3) C) local minimum at (-1, -6) local maximum at (1, 6) local minimum at (3, -3)

B) local minimum at (-0.61, -5.64) local maximum at (1.41, 6.12) local minimum at (3, -3) D) local minimum at (-3, -3) local maximum at (-1.32, 5.64) local minimum at (0.57, -6.12)

Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

Solve.

169) John owns a hotdog stand. He has found that his profit is represented by the equation P(x) = -x2 + 58x + 78, with P being profits and x the number of hotdogs sold. How many hotdogs must he sell to earn the most profit? A) 24 hotdogs B) 49 hotdogs C) 30 hotdogs D) 29 hotdogs Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

170) Bob owns a watch repair shop. He has found that the cost of operating his shop is given by c(x) = 4x2 - 360x + 61, where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? A) 40 watches B) 45 watches C) 30 watches D) 61 watches Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

171) John owns a hotdog stand. His profit is represented by the equation P(x) = -x2 + 12x + 45, with P being profits and x the number of hotdogs sold. What is the most he can earn? A) $63 B) $36 C) $117 D) $81 Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

172) A rock falls from a tower that is 49 m high. As it is falling, its height is given by the formula h(t) = 49 - 4.9t2 . How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth. A) 7 sec B) 10.2 sec C) 500 sec D) 3.2 sec Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

173) A projectile is thrown upward so that its distance above the ground after t seconds is h(t) = -16t2 + 546t. After how many seconds does it reach its maximum height? Round to the nearest second. A) 17 sec B) 31.5 sec C) 10 sec D) 42 sec Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

174) A rock falls from a tower that is 464 ft high. As it is falling, its height is given by the formula h(t) = 464 - 16t2 . How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth. A) 5.4 sec B) 29.2 sec C) 21.5 sec D) 13,456 sec Objective: (2.3) Use Graphing Utility to Approximate Local Maxima/Minima and to Determine Where Function Is Incrs/Decrs

For the function, find the average rate of change of f from 1 to x: f(x) - f(1) ,x≠1 x-1 175) f(x) = -6x A) -6

-6 x-1

C) -7

D) 0

C) x2 + x + 2

x3 + x + 2 x-1

C) -

1 x+8

9 (x - 1)(x + 8)

x + 24 - 5 x+1

x + 24 + 5 x+1

Objective: (2.3) Find the Average Rate of Change of a Function

176) f(x) = x3 + x B) x2 + 2

A) 1

Objective: (2.3) Find the Average Rate of Change of a Function

177) f(x) = A)

9 x+8 9 x(x + 8)

1 x+8

Objective: (2.3) Find the Average Rate of Change of a Function

178) f(x) = A)

x + 24 x + 24 - 5 x-1

x + 24 + 5 x-1

Objective: (2.3) Find the Average Rate of Change of a Function

Find the average rate of change for the function between the given values. 179) f(x) = 3x - 6; from 1 to 2 A) 6 B) -6 C) 3 Objective: (2.3) Find the Average Rate of Change of a Function

D) -3

180) f(x) = x2 + 7x; from 2 to 6 A) 13

39 2

C) 10

D) 15

Objective: (2.3) Find the Average Rate of Change of a Function

181) f(x) = 1x 3 - 4x2 + 2; from -6 to 6 A) 36

B) 72

37 3

37 6

C) 2

1 3

Objective: (2.3) Find the Average Rate of Change of a Function

182) f(x) =

2x; from 2 to 8

A) 7

B) -

3 10

Objective: (2.3) Find the Average Rate of Change of a Function

183) f(x) =

3 ; from 4 to 7 x-2

A) 2

B) 7

1 3

D) -

3 10

Objective: (2.3) Find the Average Rate of Change of a Function

7 184) f(x) = 4x2 ; from 0 to 4 A) 2

1 3

C) -

3 10

D) 7

Objective: (2.3) Find the Average Rate of Change of a Function

185) f(x) = -3x2 - x; from 5 to 6 A) -2

B) -

1 6

1 2

D) -34

1 2

D) -28

Objective: (2.3) Find the Average Rate of Change of a Function

186) f(x) = x3 + x2 - 8x - 7; from 0 to 2 A) -2

B) -

1 6

Objective: (2.3) Find the Average Rate of Change of a Function

187) f(x) =

2x - 1; from 1 to 5 1 A) 6

B) -28

C) -2

Objective: (2.3) Find the Average Rate of Change of a Function

1 2

188) f(x) =

3 ; from 1 to 4 x+2

A) -

1 6

B) -2

1 2

D) -28

Objective: (2.3) Find the Average Rate of Change of a Function

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). 189) f(x) = x2 - 2x A) y = x - 2

B) y = -x + 2

C) y = x + 2

D) y = -x - 2

Objective: (2.3) Find the Average Rate of Change of a Function

190) f(x) =

8 x+7

A) y =

1 8 x+ 9 9

B) y =

1 5 x+ 9 4

C) y =

8 1 x+ 9 9

D) y = -

1 10 x+ 9 9

Objective: (2.3) Find the Average Rate of Change of a Function

191) f(x) = x + 48 A) y = (5 2 - 7)x - 5 2 + 14 C) y = (-5 2 + 7)x + 5 2 - 14

B) y = (5 2 - 7)x + 5 2 - 14 D) y = (-5 2 - 7)x - 5 2 + 14

Objective: (2.3) Find the Average Rate of Change of a Function

Solve the problem. 192) From April through December 2000, the stock price of QRS Company had a roller coaster ride. The chart below indicates the price of the stock at the beginning of each month during that period. Find the monthly average rate of change in price between June and September. Month Price April (x = 1) 115 May 108 June 88 July 99 August 95 September 111 October 93 November 85 December 66 A) -$7.67 per month B) $7.67 per month C) -$11.50 per month D) $11.50 per month Objective: (2.3) Find the Average Rate of Change of a Function

193) Along with incomes, people's charitable contributions have steadily increased over the past few years. The table below shows the average deduction for charitable contributions reported on individual income tax returns for the period 1993 to 1998. Find the average rate of change between 1995 and 1997. Year Charitable Contributions 1993 $1770 1994 $2390 1995 $2470 1996 $2800 1997 $3050 1998 $3190 A) $360 per year B) $290 per year C) $580 per year D) $330 per year Objective: (2.3) Find the Average Rate of Change of a Function

194) A deep sea diving bell is being lowered at a constant rate. After 10 minutes, the bell is at a depth of 600 ft. After 50 minutes the bell is at a depth of 2,000 ft. What is the average rate of lowering per minute? Round to the nearest hundredth is needed. A) 40.0 ft per minute B) 35.0 ft per minute C) 0.03 ft per minute D) 28.0 ft per minute Objective: (2.3) Find the Average Rate of Change of a Function

Match the graph to the function listed whose graph most resembles the one given. 195)

A) cube function C) reciprocal function

B) square function D) absolute value function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

196)

A) reciprocal function C) linear function

B) absolute value function D) constant function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

197)

A) cube root function C) square function

B) square root function D) cube function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

198)

A) linear function C) reciprocal function

B) square function D) absolute value function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

199)

A) linear function C) constant function

B) absolute value function D) reciprocal function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

200)

A) cube function C) square function

B) square root function D) cube root function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

201)

A) square root function C) absolute value function

B) reciprocal function D) square function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

202)

A) cube root function C) cube function

B) square root function D) square function

Objective: (2.4) Graph the Functions Listed in the Library of Functions

Graph the function. 203) f(x) = x y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

204) f(x) = x2 y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

205) f(x) = x3 y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

206) f(x) =

x y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

207) f(x) =

1 x y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

208) f(x) = x y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

209) f(x) =

x y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

210) f(x) = -1 y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph the Functions Listed in the Library of Functions

211) f(x) =

x-2 3

if x < 1 if x ≥ 1 y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph Piecewise-defined Functions

212)

f(x) = -x + 3 2x - 3

if x < 2 if x ≥ 2 y 5

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph Piecewise-defined Functions

213) f(x) =

-x + 2 x+3

x<0 x≥0 y

-5

B) y

-5

D) y

-5

Objective: (2.4) Graph Piecewise-defined Functions

214) f(x) =

x+1 -4 -x + 8

if -8 ≤ x < 6 if x = 6 if x > 6 y 10

-10

-5

-10

B) y 10

y 10

(6, 8)

(6, 7)

5 (6, 2)

-10

-5

5 -5

(6, 2) 10

-10

-5

5 -5

(6, -4)

(-8, -6)

(6, -4)

(-8, -7) -10

-10

D) y 10

y 10

(6, 8)

(6, 7)

5 (6, 2)

-10

-5

5 -5

(6, 2) 10

-10

-5

5 -5

(6, -4)

(-8, -6)

(-8, -7) -10

-10

Objective: (2.4) Graph Piecewise-defined Functions

(6, -4)

215) f(x) =

1 |x|

if -2 ≤ x < 5 if 5 ≤ x < 9

if 9 ≤ x ≤ 14 10

-10

-5

-10

B) 10

(9, 9)

(5, 5)

(14, 3.7) 5

(9, 9)

(5, 5) (9, 3) (14, 3.7)

(-2, 1)

(5, 1)

-5

(9, 3)

(-2, 1) -10

-10

(5, 1)

-5

-10

D) 10

(9, 9)

(5, 5)

(9, 3)

(9, 9)

(5, 5) (9, 3)

(14, 3.7) -10

-5 (-2, -1)

(5, -1)

(14, 3.7) x

-10

-5 (-2, -1)

-5

-10

Objective: (2.4) Graph Piecewise-defined Functions

(5, -1)

Find the domain of the function. 216) if x ≠ 0 f(x) = 4x 4 if x = 0 A) all real numbers

B) {x|x ≤ 0}

C) {0}

D) {x|x ≠ 0}

Objective: (2.4) Graph Piecewise-defined Functions

217)

1 if -7 ≤ x < -3 |x| if -3 ≤ x < 7 f(x) = 3 x if 7 ≤ x ≤ 21 A) {x|7 ≤ x ≤ 21} C) {x|-7 ≤ x ≤ 21}

B) {x|x ≥ -7} D) {x|-7 ≤ x < 7 or 7 < x ≤ 21}

Objective: (2.4) Graph Piecewise-defined Functions

Locate any intercepts of the function. 218) if x < 1 f(x) = -4x + 9 9x - 4 if x ≥ 1 A) (0, -4)

9 4 B) (0, 9), ( , 0), ( , 0) 4 9

C) (0, 9)

9 4 D) (0, -4), ( , 0), ( , 0) 4 9

C) (0, 0), (1, 0)

D) none

Objective: (2.4) Graph Piecewise-defined Functions

219)

1 if -7 ≤ x < -8 if -8 ≤ x < 7 f(x) = |x| 3 x if 7 ≤ x ≤ 30 A) (0, 0), (0, 1)

B) (0, 0)

Objective: (2.4) Graph Piecewise-defined Functions

Based on the graph, find the range of y = f(x). 220) 1 if x ≠ 0 - x f(x) = 2 if x = 0

-5

-10

-5

5 -5

(0, -5)

-10

A) (- ∞, ∞) C) (- ∞, 0) or {0} or (0, ∞)

B) (-10, 10) D) (- ∞, 0) or (0, ∞)

Objective: (2.4) Graph Piecewise-defined Functions

221) f(x) =

4 |x|

if -6 ≤ x < -3 if -3 ≤ x < 8

if 8 ≤ x ≤ 13 10

y (8, 8)

(-3, 4)5 (-6, 4) (-3, 3)

-10

-5

(13, 3.6) (8, 2.8) 5

-5

-10

A) [0, ∞)

B) [0, 8]

C) [0, 13]

Objective: (2.4) Graph Piecewise-defined Functions

D) [0, 8)

The graph of a piecewise-defined function is given. Write a definition for the function. 222) y 5 (3, 3) (-4, 2)

-5

A) f(x) = C) f(x) =

1 x 2

if -4 < x < 0

if 0 < x < 3

f(x) =

-2x x

if -4 ≤ x ≤ 0 if 0 < x ≤ 3

1 x 2

if -4 ≤ x ≤ 0

1 - x 2

if -4 < x < 0

if 0 < x < 3

f(x) =

if 0 < x ≤ 3

Objective: (2.4) Graph Piecewise-defined Functions

223) y 5

(3, 4) (5, 3)

(0, 1)

(3, 2)

-5

A) f(x) = C)

x+1 1 x+2 2

x+1 f(x) = 1 x 2

if 0 ≤ x ≤ 3 if 3 < x ≤ 5

f(x) =

x+1 1 1 x2 2

f(x) =

x+1 1 1 x+ 2 2

if 0 ≤ x ≤ 3 if 3 < x ≤ 5

Objective: (2.4) Graph Piecewise-defined Functions

if 0 ≤ x ≤ 3 if 3 < x ≤ 5 if 0 ≤ x ≤ 3 if 3 < x ≤ 5

224) y 5 (0, 4) (3, 2) (-3, 0) -5

-5

A) f(x) = C)

f(x) =

4 x+4 3

if -3 ≤ x ≤ 0

2 x 3

if 0 < x ≤ 3

f(x) = D)

3 x+4 4

if -3 ≤ x ≤ 0

3 x 2

if 0 < x ≤ 3

f(x) =

Objective: (2.4) Graph Piecewise-defined Functions

4 x+4 3

if -3 ≤ x ≤ 0

2 x+2 3

if 0 < x ≤ 3

4 x - 4 if -3 ≤ x ≤ 0 3 2 x 3

if 0 ≤ x ≤ 3

225) y 5 (0, 4) (3, 2) (-3, 0) -5

-5

f(x) = C)

f(x) =

4 x+4 3

if -3 ≤ x ≤ 0

2 x 3

if x > 0

f(x) = D)

4 x+4 3

if -3 ≤ x ≤ 0

2 x 3

if 0 < x ≤ 3

f(x) =

3 x+4 4

if -3 ≤ x ≤ 0

3 x 2

if x ≥ 0

3 x+4 4

if -3 ≤ x ≤ 0

3 x 2

if x > 0

Objective: (2.4) Graph Piecewise-defined Functions

Solve the problem. 226) If f(x) = int(2x), find f(-1.6). A) -1

B) -3

C) -2

D) -4

Objective: (2.4) Graph Piecewise-defined Functions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 227) A gas company has the following rate schedule for natural gas usage in single-family residences: Monthly service charge

$8.80

Per therm service charge 1st 25 therms Over 25 therms

$0.6686/therm $0.85870/therm

What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas. Objective: (2.4) Graph Piecewise-defined Functions