Question

NO LINKS!!!

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.

Answer 1

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).

Answer 2

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.

Step-by-step 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.