Chapter 1, Problem 76CR

(a)

To determine

To identify: the parent function f.

Explanation of Solution

Given information:

The given equation is $h(x)=|2x+8|-1$

The parent function of the given equation is $f(x)=\left|x\right|$ .

(b)

To determine

To describe: the sequence of transformations from f to h.

Explanation of Solution

Given information:

The given equation is $h(x)=|2x+8|-1$

The parent function of the given equation is $f(x)=\left|x\right|$ .

The sequence of transformations from f to h

Vertical stretch by the factor two $\Rightarrow f(2x)=\left|2x\right|$

left shift of $8$ units $\Rightarrow f(2x+8)=|2x+8|$

down shift of $1$ unit $\Rightarrow f(2x+8)-1=f(2x+8)-1=h(x)$

(c)

To determine

To sketch: the graph of the h by hand.

Explanation of Solution

Given information:

The given equation is $h(x)=|2x+8|-1$

The graph of the h is given below

  

(d)

To determine

To write: the function h in terms of f.

Explanation of Solution

Given information:

The given equation is $h(x)=|2x+8|-1$

The parent function of the given equation is $f(x)=\left|x\right|$ .

  $\begin{array}{l}h(x)=|2x+8|-1\\ h(x)=f(2x+8)-1\end{array}$

Hence,

The function h in terms of f is $h(x)=f(2x+8)-1$