Answer
The graph represents a function.
Domain: $[-3, 2]$
Range: $[-2, -2] \cup (0, 3]$
Work Step by Step
All vertical lines will pass through at most one point on the graph. (Note that at x=-1, the line will pass through (-1, -2), a solid dot, but not through (-1, 0), a hole or hollow dot).
Thus, the graph pass the vertical line test which means that it represents a function.
The x-values vary from -3 to 2 so the domain is $[-3, 2]$.
The y-values range from 0 to 3 (but not including 0), and also includes -2.
Thus, the range is $(-1, 2] \cup [-2,-2]$