Chapter 3.7, Problem 44E

(a)

To determine

To explain: the given function related to $y=\left|x\right|$ .

Explanation of Solution

Given information:

The function

  $y=\left|x\right|+k$

The graph of $y=\left|x\right|+k$ is the vertical up shift of the $y=\left|x\right|.;k\ge 0$

The graph of $y=\left|x\right|+k$ is the vertical down shift of the $y=\left|x\right|.k<0$

(b)

To determine

To explain: the given function related to $y=\left|x\right|$ .

Explanation of Solution

Given information:

The function

  $y=|x-h|$

The graph of $y=|x-h|$ is the horizontal right shift of the $y=\left|x\right|.;k\ge 0$

The graph of $y=|x-h|$ is the horizontal left shift of the $y=\left|x\right|.k<0$

(c)

To determine

To explain: the given function related to $y=\left|x\right|$ .

Explanation of Solution

Given information:

The function

  $y=a\left|x\right|$

The graph of $y=a\left|x\right|$ is the vertical stretch of the $y=\left|x\right|.;\left|a\right|>1,a\ge 0$

The graph of $y=a\left|x\right|$ is the vertical stretch of the $y=\left|x\right|;0<\left|a\right|<1;a\ge 0$

The graph of $y=a\left|x\right|$ is the vertical followed by reflection across x - axis of the

  $y=\left|x\right|.;\left|a\right|>1,a<0$

The graph of $y=a\left|x\right|$ is the vertical followed by reflection across x - axis of the

  $y=\left|x\right|;0<\left|a\right|<1;a<0$

(d)

To determine

To explain: the given function related to $y=\left|x\right|$ .

Explanation of Solution

Given information:

The function

  $y=\left|ax\right|$

The graph of $y=\left|ax\right|$ is the horizontal compression of the $y=\left|x\right|.;\left|a\right|>1$

The graph of $y=\left|ax\right|$ is the horizontal stretch of the $y=\left|x\right|;0<\left|a\right|<1$