Answer
See graph.
Work Step by Step
We graph:
$f(x)=\left\{\begin{array}{l}
-2x~~~~~~~~\mathrm{i}\mathrm{f}~~-3\leq x\lt -1\\
x^{2}+1~~~~~\mathrm{i}\mathrm{f}~~-1\leq x\leq 2\\
\frac{1}{2}x^{3}+1~~\mathrm{i}\mathrm{f}~~2\lt x\leq 3
\end{array}\right.$
