1. **State the problem:** We need to evaluate the composition $g(f(9))$, which means first find $f(9)$ and then find $g$ of that result. 2. **Analyze $f(x)$:** From the description, $f(x)$ is piecewise linear forming a triangle with points $(-9,0)$, $(0,9)$, and $(9,-3)$. 3. **Find $f(9)$:** Since $9$ is at the right endpoint, $f(9) = -3$. 4. **Analyze $g(x)$:** $g(x)$ is a parabola opening upwards with vertex at approximately $(0,-9)$. 5. **Find $g(f(9)) = g(-3)$:** We need to find $g(-3)$. 6. **Estimate $g(-3)$:** Since the vertex is at $(0,-9)$ and the parabola opens upwards, and $g(0) = -9$, the value at $x=-3$ is higher than $-9$. From the graph description, $g(x)$ ranges roughly from $-10$ to $9$. 7. **Using symmetry of parabola:** The vertex is at $x=0$, so $g(-3) = g(3)$. 8. **Find $g(3)$:** From the graph, $g(3)$ is approximately $0$ (since the parabola crosses near $0$ at $x=3$). 9. **Therefore, $g(-3) \approx 0$ and so $g(f(9)) = 0$. **Final answer:** $$g(f(9)) = 0$$