Chapter 1, Problem 15CT

a.

To determine

To identify : the parent function.

Answer to Problem 15CT

The parent function is $f\left(x\right)=\left|x\right|$.

Explanation of Solution

Given information :

The function is $g\left(x\right)=4|-x|-7$.

form the function provided in the question it can be observed that the function is transformed by the parent function of $f\left(x\right)=\left|x\right|$.

b.

To determine

To describe : the sequence of transformations $f$ to $g$.

Answer to Problem 15CT

reflect it in the y -axis, then stretch vertically by a factor of $4$ , then shift $7$ unit downwards.

Explanation of Solution

Given information :

The function is $g\left(x\right)=4|-x|-7$.

since parent function is $f\left(x\right)=\left|x\right|$ ,to transform the graph form $f$ to $g$ , first reflect it in the y -axis then stretch vertically by a factor of $4$ and then shift $7$ unit downwards.

c.

To determine

To draw : the graph of function g.

Explanation of Solution

Given information :

The function is $g\left(x\right)=4|-x|-7$.

graph : first, to graph the parent function use the point plotting,

x	1	-2	-3	-4
y	1	2	3	4

Now first reflect it in the y -axis then stretch vertically by a factor of $4$ and then shift $7$ unit downwards.

Thus, the graph can be obtained as: