Answer
$g(x)=\left\{
\begin{array}{cc}
-2x-7,& \quad \text{if }x\lt -2\\
2x+1, & \quad \text{if }x \geq -2
\end{array}
\right.$
Work Step by Step
The absolute value function $g(x)=a|x-h|+k$ can be written as a piecewise function.
$g(x)=\left\{
\begin{array}{cc}
a[-(x-h)]+k,& \quad \text{if }x-h\lt 0 \\
a(x-h)+k, & \quad \text{if }x-h \geq 0
\end{array}
\right.$
Given $y=g(x)=2|x+2|-3$
$\implies a=2, h=-2$ and $k=-3$
Then, $g(x)$ as a piecewise function is
$g(x)=\left\{
\begin{array}{cc}
2[-(x+2)]-3,& \quad \text{if }x+2\lt 0 \\
2(x+2)-3, & \quad \text{if }x+2 \geq 0
\end{array}
\right.$
Simplifying, we get
$g(x)=\left\{
\begin{array}{cc}
-2x-7,& \quad \text{if }x\lt -2\\
2x+1, & \quad \text{if }x \geq -2
\end{array}
\right.$
