Answer
$g(x)=\left\{
\begin{array}{cc}
5x-40,& \quad \text{if }x\lt 8\\
-5x+40, & \quad \text{if }x \geq 8
\end{array}
\right.$
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 $y=g(x)=-5|x-8|$
$\implies a=-5, h=8$ and $k=0$
Then, $g(x)$ as a piecewise function is
$g(x)=\left\{
\begin{array}{cc}
-5[-(x-8)]+0,& \quad \text{if }x-8\lt 0 \\
-5(x-8)+0, & \quad \text{if }x-8 \geq 0
\end{array}
\right.$
Simplifying, we get
$g(x)=\left\{
\begin{array}{cc}
5x-40,& \quad \text{if }x\lt 8\\
-5x+40, & \quad \text{if }x \geq 8
\end{array}
\right.$
