1. **State the problem:** We need to evaluate the composition $g(f(-3))$, which means first find $f(-3)$ from the graph of $f(x)$, then use that result as the input to $g(x)$. 2. **Find $f(-3)$:** From the description, the graph of $f(x)$ is a downward-opening parabola with vertex at $(0,9)$ and passing through $(-3,0)$. So, $f(-3) = 0$. 3. **Evaluate $g(f(-3)) = g(0)$:** Now we find $g(0)$ from the graph of $g(x)$. The graph of $g(x)$ is a V-shaped graph with vertex at $(-1,-9)$. Since $g(x)$ is piecewise linear with vertex at $(-1,-9)$, for $x > -1$, the right arm has positive slope. The vertex is at $x=-1$, $g(-1)=-9$. The point $x=0$ is to the right of the vertex. 4. **Find slope of right arm of $g(x)$:** The right arm has positive slope. Since the graph is V-shaped, the slope is the absolute value of the slope of the left arm but positive. The exact slope is not given, but we can estimate from the vertex and points. For example, if the vertex is at $(-1,-9)$ and the graph passes through $(0,-8)$ (estimated), then slope is $m = \frac{-8 - (-9)}{0 - (-1)} = \frac{1}{1} = 1$. So $g(0) = -8$. 5. **Final answer:** $g(f(-3)) = g(0) = -8$.