Answer
See graph.
Work Step by Step
Step 1. Graph $f(x)=x^3+3$ with $-2\le x \le 0$ as shown in the figure (red curve).
Step 2. Graph $f(x)=x+3$ with $0\lt x \lt1$ as shown in the figure (blue line).
Step 3. Graph $f(x)=4+x-x^2$ with $1\le x \le3$ as shown in the figure (green curve).