The graph provided represents the function $f(x)$ on the interval $[-9, 9]$. To find the absolute maximum value of $f(x)$, we need to identify the highest point on the graph over the given interval.

From analyzing the graph:

1. At $x = -9$, $f(x) = 4$.
2. The graph rises to a peak at $x = -3$, where $f(x) = 5$.
3. At other points, $f(x)$ does not exceed this value of 5.

Conclusion:

The absolute maximum value of $f(x)$ is 5, which occurs at $x = -3$.

Let me know if you'd like detailed steps or have further questions!

Related Questions:

1. What is the absolute minimum value of $f(x)$ on the interval $[-9, 9]$?
2. How can you determine local extrema from a graph visually?
3. What is the difference between absolute and local extrema?
4. How do endpoints of a graph affect the absolute extrema?
5. Could $f(x)$ have different absolute extrema if the domain were restricted?

Tip:

Always consider both critical points and endpoints when finding absolute extrema of a function!