1-5 Parent Functions And Transformations Worksheet With Answers Page 15

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ANSWER:  
3
ANSWER:  
Sometimes; sample answer: f (x) = x
is an odd
function and f (–x) ≠ –| f (x)| when x = –1. However, f
Sample answer: Both; for the greatest integer
(x) = 0 is an odd function and f (–x) = –| f (x)| for all x
function, a shift of a units left is identical to a shift of
1-5 Parent Functions and Transformations
a units up.
74. 
78. 
REASONING Let f (x) be an odd function. If g(x)
If f (x) is an even function, then f (−x) = −| f (x)|.
is a reflection of f (x) in the x-axis and h(x) is a
ANSWER:  
reflection of g(x) in the y-axis, what is the
Sometimes; sample answer: f (x) = –| x |  is an even 
relationship between f (x) and h(x)? Explain.
function and f (x) = –| f (x)|  for all x. However, f (x) =
ANSWER:  
| x | is an even function and f (x) ≠ –| f (x)| when x =
0. 
f(x) and g(x) represent the same function; sample
3
answer: If f (x) = x
, an odd function, then g(x) =
79. 
CHALLENGE Describe the transformation of f (x)
3
−x
, a reflection of f (x) in the y-axis. Likewise, h(x)
=
if (−2, −6) lies on the curve.
3
3
= −(−x
) or x
, a reflection of g(x) in the x-axis.
Therefore, f (x) = h(x).
ANSWER:  
Sample answer: The graph of g(x) =
 is the
75. 
Writing in Math Explain why order is important
graph of f (x) =
translated 6 units to the left and 8
when transforming a function with reflections and
translations.
units down.
ANSWER:  
80. 
REASONING   Suppose (a, b) is a point on the
Sample answer: Order is important because different
graph of f (x). Describe the difference between the
graphs can be obtained depending on the order the
transformations of (a, b) when the graph of f (x) is
transformations are performed. For example, if (a,
expanded vertically by a factor of 4 and when the
b) is on the original graph and there is a translation 6
graph of f (x) is compressed horizontally by a factor
units up and then a reflection in the x-axis, the
of 4.
resulting point will be (a, −b – 6). However, if (a, b)
ANSWER:  
is reflected in the x-axis first and then translated 6
Sample answer: A vertical expansion of f (x) by a
units up, the resulting point will be (a, −b + 6).
factor of 4 would move (a, b) to (a, 4b). A
4
horizontal compression by a factor of
would move
REASONING Determine whether the following
statements are sometimes, always, or never
(a, b) to
.
true. Explain your reasoning.
76. 
If f (x) is an even function, then f (x) = | f (x)|.
81. 
Writing in Math Use words, graphs, tables, and
ANSWER:  
equations to relate parent functions and
Sometimes; sample answer: If f (x) is even and all
transformations. Show this relationship through a
values of f (x) are nonnegative, then
specific example.
2
f(x) = | f (x)|. However, g(x) = x
− 4is even, but g
ANSWER:  
(−1) ≠ |g(−1)|.
See students’ work.
77. 
If f (x) is an odd function, then f (−x) = −| f (x)|.
Find the average rate of change of each
function on the given interval.
ANSWER:  
2
82. 
g(x) = −2x
+ x – 3; [−1, 3]
3
Sometimes; sample answer: f (x) = x
is an odd
ANSWER:  
function and f (–x) ≠ –| f (x)| when x = –1. However, f
(x) = 0 is an odd function and f (–x) = –| f (x)| for all x
−3
2
83. 
78. 
g(x) = x
– 6x + 1; [4, 8]
If f (x) is an even function, then f (−x) = −| f (x)|.
ANSWER:  
ANSWER:  
6
Sometimes; sample answer: f (x) = –| x |  is an even 
function and f (x) = –| f (x)|  for all x. However, f (x) =
3
2
| x | is an even function and f (x) ≠ –| f (x)| when x =
84. 
f (x) = −2x
– x
+ x – 4; [−2, 3]
0. 
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Page 15
ANSWER:  
79. 
CHALLENGE Describe the transformation of f (x)
−14

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