1. **State the problem:** We need to evaluate $f(g(-3))$, which means first find $g(-3)$ and then substitute that result into $f(x)$. 2. **Analyze $g(x)$:** The graph of $g(x)$ is a V-shaped absolute value function with vertex at $(0, -9)$ and lines $y = x - 9$ for $x \geq 0$ and $y = -x - 9$ for $x \leq 0$. Since $-3 \leq 0$, we use the line $y = -x - 9$. 3. **Calculate $g(-3)$:** $$g(-3) = -(-3) - 9 = 3 - 9 = -6$$ 4. **Analyze $f(x)$:** The graph of $f(x)$ is a parabola opening upwards with vertex at $(-6, -6)$. Since the vertex is at $(-6, -6)$, the value of $f(-6)$ is $-6$. 5. **Calculate $f(g(-3)) = f(-6)$:** $$f(-6) = -6$$ **Final answer:** $$f(g(-3)) = -6$$