Chapter 1.2, Problem 29E

Solution

To identify: graph the function and intervals on which the function is increasing,

decreasing, or constant.

The function is decreasing on $(-\infty ,-2]$ and increasing on $[-2,\infty )$ .

Given information: 

The function $f\left(x\right)=\left|x+2\right|-1$ .

Calculation:

Graph of

  $f\left(x\right)=\left|x+2\right|-1$

Let $y=f\left(x\right)$ .

Putting the value of then

And $x=-2$ then $y=-1$

And $x=-4$ then $y=1$

And $x=\infty$ then $y=\infty$ .

Plot the graph

  

Therefore, the function decreases in the interval $(-\infty ,-2]$ and increases in the interval $[-2,\infty )$ .