Subjects algebra

Visual Composition 748779

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1. **State the problem:** We want to find the visual composition $g(f(9))$ using the given graphs of $f$ and $g$. 2. **Identify $f(9)$ from the graph:** From the piecewise linear graph of $f$, at $x=9$, the value is $f(9) = -3$. 3. **Identify $g(f(9)) = g(-3)$ from the graph:** Using the parabola graph of $g$, find the value at $x = -3$. 4. **Estimate $g(-3)$:** The parabola is symmetric about $x=0$ with vertex at $(0,-9)$, so $g(-3) = g(3)$. 5. **Find $g(3)$ from the graph:** At $x=3$, $g(3)$ is approximately $0$. 6. **Conclusion:** Therefore, $g(f(9)) = g(-3) = 0$. **Final answer:** $$g(f(9)) = 0$$