Chapter 1.6, Problem 40E

Solution

a.

The vertical stretch by a factor of 2 in function $f\left(x\right)=\left|x+2\right|$ .

The function after vertical stretch by a factor of 2 is $2\left|x+2\right|$ .

Given:

  $f\left(x\right)=\left|x+2\right|$

Calculation:

  $f\left(x\right)=\left|x+2\right|$

Vertical stretch by a factor of 2:

  $2f\left(x\right)=2\left|x+2\right|$

b.

The horizontal shrink by a factor of $\frac{1}{3}$ in function $f\left(x\right)=\left|x+2\right|$ .

The function after horizontal shrink by a factor of $\frac{1}{3}$ is $\left|3x+2\right|$ .

Given:

  $f\left(x\right)=\left|x+2\right|$

Calculation:

  $f\left(x\right)=\left|x+2\right|$

Horizontal shrink by a factor of $\frac{1}{3}$ :

  $\begin{array}{l}f\left(\frac{x}{\frac{1}{3}}\right)=f\left(3x\right)\\ f\left(\frac{x}{\frac{1}{3}}\right)=\left|3x+2\right|\end{array}$