1-5 Parent Functions And Transformations Worksheet With Answers Page 14
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181-5 Parent Functions and Transformations
70.
72.
MULTIPLE REPRESENTATIONS In this
g(x) = f (4x) – 5
problem, you will investigate operations with
ANSWER:
2
functions. Consider f (x) = x
+ 2x + 7, g(x) = 4x + 3,
2
g(x) =
− 9
and h(x) = x
+ 6x + 10.
a. TABULAR Copy and complete the table below
for three values for a.
b. VERBAL How are f (x), g(x), and h(x) related?
c. ALGEBRAIC Prove the relationship from part b
algebraically.
71.
g(x) = f (2x + 1) + 8
ANSWER:
ANSWER:
a.
g(x) =
+ 4
b. Sample answer: h(x) is the sum of f (x) and g(x).
c.
73.
ERROR ANALYSIS Danielle and Miranda are
72.
MULTIPLE REPRESENTATIONS In this
describing the transformation g(x) = [[x + 4]].
problem, you will investigate operations with
Danielle says that the graph is shifted 4 units to the
2
functions. Consider f (x) = x
+ 2x + 7, g(x) = 4x + 3,
left, while Miranda says that the graph is shifted 4
2
and h(x) = x
+ 6x + 10.
units up. Is either of them correct? Explain.
a. TABULAR Copy and complete the table below
ANSWER:
for three values for a.
Sample answer: Both; for the greatest integer
function, a shift of a units left is identical to a shift of
a units up.
74.
REASONING Let f (x) be an odd function. If g(x)
is a reflection of f (x) in the x-axis and h(x) is a
b. VERBAL How are f (x), g(x), and h(x) related?
reflection of g(x) in the y-axis, what is the
c. ALGEBRAIC Prove the relationship from part b
relationship between f (x) and h(x)? Explain.
algebraically.
ANSWER:
ANSWER:
f(x) and g(x) represent the same function; sample
3
a.
answer: If f (x) = x
, an odd function, then g(x) =
3
−x
, a reflection of f (x) in the y-axis. Likewise, h(x)
3
3
= −(−x
) or x
, a reflection of g(x) in the x-axis.
Therefore, f (x) = h(x).
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Page 14
75.
Writing in Math Explain why order is important
b. Sample answer: h(x) is the sum of f (x) and g(x).
when transforming a function with reflections and
c.
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