Exercise 17 Page 160

Let's graph $y(x)$ first and then we can compare it to the graph of $f(x).$

Graphing $y(x)$

To graph the function without going through the entire process of transforming the parent function, we can make a table of values. Then we only need to plot the ordered pairs that we find.

$x$	$\left|x+4\right|-2$	Simplify	$y(x)$
$\text{-}8$	$\left|\text{-}8+4\right|-2$	$|\text{-}4|-2$	$2$
$\text{-}6$	$\left|\text{-}6+4\right|-2$	$|\text{-}2|-2$	$0$
$\text{-}4$	$\left|\text{-}4+4\right|-2$	$|0|-2$	$\text{-}2$
$\text{-}2$	$\left|\text{-}2+4\right|-2$	$|2|-2$	$0$
$0$	$\left|0+4\right|-2$	$|4|-2$	$2$

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of $y(x).$ Note that $y(x)$ is a transformation of the graph of the parent function $y=|x|,$ which is V-shaped. Therefore, $y(x)$ will also be a V-shaped graph.