1. **Problem Statement:** We are given a function $f(x)$ defined on the interval $[-9,9]$ with specific points on its graph. We need to find the $x$-value(s) where the global maximum of $f(x)$ occurs. 2. **Understanding Global Maximum:** The global maximum of a function on a closed interval is the highest value the function attains anywhere on that interval. 3. **Given Points:** The function passes through these points: - $(-9, -4)$ - $(-7, 5)$ - $(-4, 1)$ - $(-1, -8)$ - $(3, -1)$ - $(7, -4)$ 4. **Finding the Maximum Value:** We compare the $y$-values of these points to find the highest one: - $-4, 5, 1, -8, -1, -4$ 5. **Maximum $y$-value:** The highest $y$-value is $5$ at $x = -7$. 6. **Conclusion:** The global maximum value of $f(x)$ is $5$, and it occurs at $x = -7$. **Final answer:** $$x = -7$$