Answer
$g(x)=\left\{
\begin{array}{cc}
-4x+4,& \quad \text{if }x\lt 1\\
4x-4, & \quad \text{if }x \geq 1
\end{array}
\right.$
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 $y=g(x)=4|x-1|$
$\implies a=4, h=1$ and $k=0$
Then, $g(x)$ as a piecewise function is
$g(x)=\left\{
\begin{array}{cc}
4[-(x-1)]+0,& \quad \text{if }x-1\lt 0 \\
4(x-1)+0, & \quad \text{if }x-1 \geq 0
\end{array}
\right.$
Simplifying, we get
$g(x)=\left\{
\begin{array}{cc}
-4x+4,& \quad \text{if }x\lt 1\\
4x-4, & \quad \text{if }x \geq 1
\end{array}
\right.$
