Answer
See graph.
Work Step by Step
Step 1. Graph $f(x)=-2x$ with $-3\le x \lt-1$ as shown in the figure (red line).
Step 2. Graph $f(x)=x^2+1$ with $-1\le x \le2$ as shown in the figure (blue curve).
Step 3. Graph $f(x)=\frac{1}{2}x^3$ with $2\lt x \le3$ as shown in the figure (green curve).