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The function g is related to one of the parent functions.
g(x) = - ( x - 4)^3

a. Identify the parent function f.
f(x)= __________
b. Describe the sequence of transformations from f to g. (Select all that apply.)
1. vertical shrink
2. reflection in the x-axis
3. vertical stretch
4. horizontal shift of 4 units right
5. vertical of 4 units upward

c. Sketch the graph of g.

User Bowsie
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2 Answers

6 votes

Answer:


\textsf{a)} \quad f(x)=x^3

b) 4. horizontal shift of 4 units right

2. reflection in the x-axis

c) See attachment.

Explanation:

Part (a)

Given function:


g(x)=-(x-4)^3

The parent function is:


f(x)=x^3

Part (b)

To transform the parent function f(x) to g(x):

1. Horizontal shift of 4 units right:


\implies f(x-4) = (x-4)^3

2. Reflection in the x-axis:


\implies -f(x-4) = -(x-4)^3

Part (c)

To sketch the graph of g(x):

  • Sketch the graph of y = x³
  • Translate it 4 units to the right.
  • Reflect it in the x-axis.
NO LINKS!!! The function g is related to one of the parent functions. g(x) = - ( x-example-1
User Maymay
by
8.6k points
5 votes

Given function:

  • g(x) = - (x - 4)³

This is a transformation of the

  • a) parent cubic function f(x) = x³

b)

It was first reflected in the x-axis:

  • f (x) → h(x) ⇒ x³ → - x³

Then translated right by 4 units:

  • h(x) → g(x) ⇒ - x³ → - (x - 4)³

So the applicable choices are:

  • 2. reflection in the x-axis,
  • 4. horizontal shift of 4 units right.

c)

See the attached with all transformations f(x) → h(x) → g(x).

NO LINKS!!! The function g is related to one of the parent functions. g(x) = - ( x-example-1
User MStrutt
by
7.9k points

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