College Algebra 9th txtbk

Review Exercises 255
66. The following graph is the result of applying a sequence of transformations
to the graph of y x 2 . Describe the transformations
verbally and write an equation for the given graph.
Check by graphing your equation on a graphing calculator.
(A)
y
5
5
y
5
5
x
5
5
5
x
(B)
y
5
5
67. The graph of f (x) x is vertically stretched by a factor of 3,
reflected through the x axis, and shifted 2 units to the right and
5 units up to form the graph of the function g. Find an equation
for the function g and graph g.
68. Write an equation for the following graph in the form
y a(x h) 2 k, where a is either 1 or 1 and h and k are
integers.
Check by graphing your equation on a graphing calculator.
5
69. The following graph is the result of applying a sequence of
transformations to the graph of y 1 3 x. Describe the transformations
verbally, and write an equation for the given
graph.
5
5
5
5
5
Check by graphing your equation on a graphing calculator.
70. How is the graph of f(x) (x 2) 2 1 related to the graph of
g(x) x 2 ?
71. Each of the following graphs is the result of applying one
or more transformations to the graph of one of the six basic functions
in Figure 1, Section 3-3. Find an equation for the graph.
Check by graphing the equation on a graphing calculator.
y
y
5
5
x
x
5
5
5
72. The graph of f (x) x is stretched vertically by a factor of 3,
reflected through the x axis, shifted four units to the right and
eight units up to form the graph of the function g. Find an equation
for the function g and graph g.
73. The graph of m(x) x 2 is stretched horizontally by a factor of 2,
shifted two units to the left and four units down to form the graph
of the function t. Find an equation for the function t and graph t.
Use graph transformations to sketch the graph of each equation in
Problems 74–81:
74. y x 1
75. y 1 1 3 1 x
76. y x 2
77. y 9 31x
78. y 1 2
x
79. y 1 3 4 0.5x
80. y 2 3(x 1) 3 81. y x 1 1
Solve Problems 82 and 83. Express answers in interval notation.
82. x 2 x 6 20 83. x 2 7 4x 12
84. Find the domain of f (x) 225 x 2 .
85. Given f (x) x and g(x) 11 x, find each function and its
domain.
(A) fg (B) fg (C) f ° g (D) g ° f
86. For the one-to-one function f given by
(A) Find f 1 (x).
(B) Find f 1 (3).
(C) Find f 1 [ f (x)].
2
f (x) x 2
x 3
87. Given f (x) 1x 1:
(A) Find f 1 (x).
(B) Find the domain and range of f and f 1 .
(C) Graph f, f 1 , and y x on the same coordinate system.
x