Answer
The curve represents a function of $x$.
Domain: $[-3, 2]$
Range: $\left\{-2\right\} \cup \left\{y | 0 \lt y \le 3\right\}$
Work Step by Step
RECALL:
The Vertical Line test states that if all vertical lines will pass through a graph in at most one point, then the graph represents a function of $x$.
Note that all vertical lines will pass through the given graph in at most one point only. Even the vertical line that would seem to pass through two different points ($x=-1$), the vertical line actually passes through the graph at only one point since the other point is a hole, which is not really part of the graph.
Thus, the given graph represents a function of $x$.
The domain is the set of $x$ values covered by the graph, while the range is the set of $y$ values covered by the graph of the function.
The graph covers the x-values from $-3$ to $2$.
Thus, the domain is $[-3, 2]$.
The graph covers the y-values $-2$ and $0
