Chapter 6.5, Problem 52E

To determine

To graph: the inequality.

Explanation of Solution

Given information:

  $y\le \left|x+4\right|$

Calculation:

Substitute different values of x in $y=\left|x+4\right|$ and evaluate y to create a table of values for this equation as shown below.

$x$	$y$
$-$ 12	8
$-$ 10	6
$-$ 8	4
$-$4	0
$-$ 2	2
0	4
2	6
4	8
8	12
10	14
12	16

Now plot the points on the graph and join them. Since the inequality has less than or equal to sign so solid line will be used to join the point coordinates. The test points for $y\le \left|x+4\right|$ are evaluated as follows:

Test point $\left(x,y\right)$	Inequality $\left(y\le \left|x+4\right|\right)$	True/False
$\left(-2,-2\right)$	$\begin{array}{l}-2\le \left|-2+4\right|\\ -2\le 2\end{array}$	True
$\left(-4,4\right)$	$\begin{array}{l}4\le \left|-4+4\right|\\ 4\le 0\end{array}$	False

The region having the true point will be shaded as shown below. The shaded region represents the inequality, $y\le \left|x+4\right|$.