Larson, Precalculus Functions and Graphs: a Graphing Approach, 5E Chapter 1

Larson, Precalculus Functions and Graphs: A Graphing Approach, 5e Chapter 1

CHAPTER 1-IF YOU CANNOT DO ANY PROBLEM, READ CHAPTER 1 IN THE TEXT BOOK

6. / Find the slope-intercept form of the line passing through the points.
(–1, 2), (0, 8)
A) / 6x – 13 / D) /
B) / 6x + 8 / E) / –6x – 4
C) /
7. / Find the slope-intercept form of the line passing through the points.
(–1, 1), (4, 3)
A) / / D) /
B) / / E) /
C) /
8. / Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither.
L1 : (–1, 5), (6, 6)
L2 : (6, –3), (–1, –4)
A) parallel B) perpendicular C) neither
9. / Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither.
L1 : (3, 2), (–5, –5)
L2 : (–2, 0), (2, –7)
A) parallel B) perpendicular C) neither
11. / Write the slope-intercept form of the equation of the line through the given point parallel to the given line.
point: (6, 2)line: –28x – 7y = 3
A) / / D) / y = –4x + 26
B) / / E) / y = –4x + 14
C) / y = –28x – 166
12. / Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line.
point: (–2, –5)line: 6x – 24y = 6
A) / / D) / y = 6x – 17
B) / / E) /
C) / y = –4x – 13
13. / Does the table describe a function?

A) yes B) no
14. / Does the table describe a function?

A) no B) yes
15. / Does the table describe a function?

A) yes B) no
16. / Does the table describe a function?

A) yes B) no
17. / Which set of ordered pairs represents a function from P to Q?
P = {1, 2, 3, 4}Q = {–2, 0, 2}
A) / {(1, –2), (2, 0), (2, 2), (3, 0), (4, –2)}
B) / {(3, –2), (3, 0), (3, 2)}
C) / {(3, 0), (2, –2), (1, 0), (2, 2), (3, –2)}
D) / {(2, 0), (3, 2), (4, 0)}
E) / {(1, 2), (3, 0), (1, –2), (3, 2)}
18. / Which equation does not represent y as a function of x?
A) / x = –7y – 6 / D) / y = |–8 + x2|
B) / x = 8 / E) /
C) / y = –4x – 4
19. / Which equation does not represent y as a function of x?
A) / 8y = 5 / D) / –9x2 + 8y = 6
B) / –4x = –4y / E) / 2y2 – 9x = 2
C) / –3x – 8y = 4
21. / Evaluate the following function at the specified value of the independent variable and simplify.

A) –14 B) C) 3 D) –11 E) undefined
22. / Evaluate the function at the specified value of the independent variable and simplify.

g (y + 3)
A) B) C) D) E)
23. / Evaluate the following function at the specified value of the independent variable and simplify.

A) 28 B) 22 C) –53 D) 47 E) undefined
24. / Evaluate the function at the specified value of the independent variable and simplify.


A) B) C) D) E)
25. / Find all real values of x such that f (x) = 0.

A) B) C) D) E)
26. / Find all real values of x such that f (x) = 0.

A) B) C) D) E)
27. / Find the value(s) of x for which f (x) = g (x).
f (x) = x2 + 19x + 73g (x) = 2x + 1
A) 73, 54, B) 73, 19, C) –9, –8 D) 9, 8 E) –92,
28. / Find the domain of the function.
A) / all real numbers / D) / p = 4, p = 0
B) / all real numbers , / E) / p = 4
C) / all real numbers
29. / Find the domain of the function.

A) –2 s2 B) s–2 or s2 C) s0 D) s 2 E) all real numbers
30. / Find the difference quotient and simplify your answer.
f (x) = –9x2 + 6x,, h 0
A) 12 + h B) C) D) 6 – 9h E) –48 – 9h
31. / Determine a piecewise-defined function for the graph shown below.

A) /
B) /
C) /
D) /
E) /
32. / Use the graph of the function to find the domain and range of f.

A) /
B) /
C) /
D) /
E) /
33. / Use the Vertical Line Test to determine in which of the graphs y is not a function of x.
A) / x

B) / x

C) / x

D) / x

E) / All of the choices (A, B, C, and D) represent functions.
34. / Determine the intervals over which the function is increasing, decreasing, or constant.


A) /
B) /
C) /
D) /
E) /
35. / Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.

A) /
B) /
C) /
D) /
E) /
36. / Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.
f (x) = x3 – 3x2 + x + 2
A) / relative maximum:(0.18, 2.09)
relative minimum:(1.82, –0.09)
B) / relative maximum:(1.82, –0.09)
relative minimum:(0.18, 2.09)
C) / relative maximum:(2.09, 0.18)
relative minimum:(–0.09, 1.82)
D) / relative maximum:(–0.09, 1.82)
relative minimum:(2.09, 0.18)
E) / relative maximum:(–0.09, 1.89)
relative minimum:(2.09, 0.11)
37. / Determine whether the function is even, odd, or neither.

A) B) C)
LearningObjective:Identifyevenandoddfunctions
Section:1.3
38. / Algebraically determine whether the function below is even, odd, or neither.

A) even B) odd C) cannot be determined D) neither
39. / Algebraically determine whether the function below is even, odd, or neither.

A) even B) odd C) cannot be determined D) neither
40. / Graph the function and determine the interval(s) for which f (x)  0.
f (x) = –x2 – x

A) / / D) /
B) / / E) / {–1}
C) /
41. / If f is an even function, determine if g is even, odd, or neither.

A) even B) odd C) cannot be determined D) neither
42. / If f is an even function, determine if g is even, odd, or neither.

A) even B) odd C) cannot be determined D) neither
43. / Use the graph of f to sketch the graph of the function indicated below.
f

A) / D)
D
B) / E)

C)
44. / Use the graph of f to sketch the graph of the function indicated below.
f

A) / D)
B) / E)
C)
45. / Use the graph of

to write an equation for the function whose graph is shown.

A) /
B) /
C) /
D) /
E) /
46. / Compare the graph of the following function with the graph of

A) / First a vertical shift of units up then a reflection in the y-axis.
B) / First a horizontal shift of units to the left then a reflection in the y-axis.
C) / First a vertical shift of units up then a reflection in the x-axis.
D) / First a horizontal shift of units to the left, then a vertical shift of units up and then a reflection in the y-axis.
E) / First a horizontal shift of units to the left then a reflection in the x-axis.
47. / Compare the graph of the following function with the graph of

A) / vertical shift of units up
B) / horizontal stretch of units
C) / vertical shrink of units
D) / horizontal shrink of units
vertical shift of units
E) / horizontal shrink of units
48. / Compare the graph of the following function with the graph of

A) / vertical shift of units down
B) / vertical shift of units down
horizontal shrink of units
C) / horizontal shift of units to the right
horizontal shrink of units
D) / horizontal shift of units to the right
horizontal stretch of units
E) / horizontal shift of units to the right
vertical shift of units down
49. / Use function notation to write g in terms of

A) / / D) /
B) / / E) /
C) /
50. / Use function notation to write g in terms of

A) / / D) /
B) / / E) /
C) /
51. / Use function notation to write g in terms of

A) / / D) /
B) / / E) /
C) /
52. / Determine an equation that may represented by the graph shown below.

A) / / D) /
B) / / E) /
C) /
53. / Determine an equation that may represented by the graph shown below.

A) / / D) /
B) / / E) /
C) /
54. / Determine an equation that may represented by the graph shown below.

A) / / D) /
B) / / E) /
C) /
55. / Use the graphs of f and g, shown below, to graph

A)
/ D)

B)
/ E)

C)

57. / Find ( f  g )(x).

A) / / D) /
B) / / E) /
C) /
58. / Find ( fg )(x).

A) / / D) /
B) / / E) /
C) /
59. / Find ( fg )(x).

A) / / D) /
B) / / E) /
C) /
60. / Evaluate the following function for and algebraically.

A) 10 B) –2 C) 94 D) 82 E) 62
61. / Evaluate the indicated function for f (x) = x2 – 3 and g (x) = x – 4.
( fg )(–3)
A) –42 B) 84 C) –15 D) 6 E) 30
62. / Evaluate the indicated function for f (x) = x2 – 3 and g (x) = x + 2.
( f  g )(t – 6)
A) / t2 – 13t + 37 / D) / t2 – 11t + 41
B) / t2 – 13t + 41 / E) / t2 t + 37
C) / t2 – 11t + 37
63. / Evaluate the following function for and algebraically.

A) / / D) /
B) / / E) /
C) /
64. / Find
f (x) = –3x – 8g (x) =x – 9
A) / –3x + 19 / D) / –4x + 1
B) / –3x – 17 / E) / –4x – 17
C) / –3x2 + 19x + 72
65. / Find
f (x) = x + 6g (x) =x2
A) / x2 + 6 / D) / x2 + 6x + 36
B) / x2 – 36 / E) / x2 + 12x + 36
C) / x2 + 36
66. / Given that and determine the value of the following (if possible).

A) B) C) D) E) not possible
67. / Determine the domain of .
A) / / D) /
B) / / E) /
C) /
68. / Given and determine the domain of
A) / / D) /
B) / / E) /
C) /

LearningObjective:Identify rules and domain for composition of functions

Section:1.5

69. / Given and determine and the domain of
A) / ; ;
B) / ; ;
C) / ; ;
D) / ; ;
E) / ; ;
70. / Find f (x) =x + 2
A) / / D) /
B) / / E) /
C) /
71. / Find
A) / / D) /
B) / / E) /
C) /
73. / Given the following function, find two functions f and g such that
A) / / D) /
B) / / E) /
C) /
74. / Show algebraically that the functions f and g shown below are inverse functions.

Learn this:

75. / Show algebraically that the functions f and g shown below are inverse functions.

A) /
B) /
C) /
D) /
E) /
77. / Match the graph of the function shown below with the graph of its inverse function

A) /
B) /
C) /
D) /
E) /
LearningObjective:Identify the graph of the inverse of a function
Section:1.6
80. / Find the inverse function of
A) / / D) /
B) / / E) /
C) /
81. / Determine whether the function has an inverse function. If it does, find the inverse function.

A) / No inverse function exists. / D) /
B) / / E) /
C) /
82. / Find the inverse function of f.

A) / / D) /
B) / / E) /
C) /
88. / Use the functions given by and to find the indicated value.

A) B) C) D) E) undefined
Ans:B
LearningObjective:Evaluate the inverse of the composition of two functions
Section:1.6
89. / Use the functions and to find
A) / / D) /
B) / / E) /
C) /
90. / Use the functions and to find
A) / / D) /
B) / / E) /
C) /

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