Chapter 5.8, Problem 22P

Graph each translation of $y=\left|x\right|$.

Describe how the graph is related to the graph of $y=\left|x\right|$. $y=|x+3|-2$

To determine

Draw the graph of the function $y=\left|x+3\right|-2$ by translating $y=\left|x\right|$ .

Explanation of Solution

Given information:

The given function is $y=\left|x+3\right|-2$ .

Calculation:

Consider the equations $y=\left|x+3\right|-2$ and $y=\left|x\right|$ .

The equation $y=\left|x+3\right|-2$ , 3 units left and 2 units down from the equation $y=\left|x\right|$ .

So, each point of $y=\left|x+3\right|-2$ , is 3 units left and 2 units down the corresponding points of $y=\left|x\right|$ .

Thus, the translation occurs 3 units left and 2 units down with $y=\left|x\right|$ .

The graph of the equation is:

  

Hence, a translation occurs 3 units left and 2 units down with $y=\left|x\right|$ .