1. The problem asks to evaluate $f(-2)$ for the given piecewise function. 2. From the graph description, the function has a horizontal line segment from $x=-2$ to $x=2$ at $y=-4$, but the point at $x=-2$ is an open point at $(-2,-4)$, meaning $f(-2)$ is not equal to $-4$. 3. Since the point at $x=-2$ is open at $y=-4$, we must check if there is a defined value at $x=-2$ elsewhere. 4. The graph description does not mention a solid point at $x=-2$ other than the open point at $(-2,-4)$. 5. Therefore, $f(-2)$ is undefined because the function is not defined at $x=-2$ (open point means no value). Final answer: $f(-2)$ is undefined.