Answer
a) $f(x)=\left\{\begin{array}{lll}2 x-6 & \text { for } & x \geq 3 \\ 6-2 x & \text { for } & x<3\end{array}\right.$
b) See the graph.
Work Step by Step
a) We have $$
f(x)=\left\{\begin{array}{lll}
2 x-6 & \text { for } & 2 x-6 \geq 0 \\
-(2 x-6) & \text { for } & 2 x-6<0
\end{array}\right.
$$ or $$
f(x)=\left\{\begin{array}{lll}
2 x-6 & \text { for } & x \geq 3 \\
6-2 x & \text { for } & x<3
\end{array} .\right.
$$
b) We draw each branch. See graph.
