Answer
$g(x)=\left\{
\begin{array}{cc}
-2x-6,& \quad \text{if }x\lt -3\\
2x+6, & \quad \text{if }x \geq -3
\end{array}
\right.$
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 $y=g(x)=2|x+3|$
$\implies a=2, h=-3$ and $k=0$
Then, $g(x)$ as a piecewise function is
$g(x)=\left\{
\begin{array}{cc}
2[-(x+3)]+0,& \quad \text{if }x+3\lt 0 \\
2(x+3)+0, & \quad \text{if }x+3 \geq 0
\end{array}
\right.$
Simplifying, we get
$g(x)=\left\{
\begin{array}{cc}
-2x-6,& \quad \text{if }x\lt -3\\
2x+6, & \quad \text{if }x \geq -3
\end{array}
\right.$
