1. **State the problem:** We need to find the absolute maximum value of the function $f$ on the interval $[-9,8]$. 2. **Recall the definition:** The absolute maximum of a function on a closed interval is the highest value $f(x)$ attains at any point $x$ in that interval, including endpoints and critical points. 3. **Identify critical points and endpoints in the interval:** From the graph description, within $[-9,8]$, the function has peaks near $x=-8$ with $f(-8)=7$, near $x=-3$ with $f(-3)=6$, and near $x=2$ with $f(2)=11$. The endpoints are $x=-9$ and $x=8$; the graph near $x=-9$ is close to the peak at $-8$, and near $x=8$ the function is about $6$. 4. **Evaluate $f$ at these points:** - $f(-8) = 7$ - $f(-3) = 6$ - $f(2) = 11$ - $f(-9)$ is slightly less than $7$ (since peak is at $-8$) - $f(8)$ is about $6$ 5. **Compare values:** The highest value among these is $f(2) = 11$. 6. **Conclusion:** The absolute maximum of $f$ on $[-9,8]$ is $11$ at $x=2$. **Final answer:** $$\boxed{\text{The absolute maximum of } f \text{ is } f(2) = 11.}$$