To find the average rate of change of the function $f(x)$ on the interval $[-8, -3]$, we use the formula:

$\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}$

where $a = -8$ and $b = -3$. From the graph, we need to identify $f(-8)$ and $f(-3)$:

1. At $x = -8$, $f(-8) \approx 40$.
2. At $x = -3$, $f(-3) \approx -10$.

Now we substitute these values into the formula:

$\text{Average rate of change} = \frac{f(-3) - f(-8)}{-3 - (-8)} = \frac{-10 - 40}{-3 + 8} = \frac{-50}{5} = -10$

Thus, the average rate of change on the interval $[-8, -3]$ is -10.

Would you like further clarification, or do you have any other questions?

Here are 5 related questions you might find useful:

1. What does a negative average rate of change indicate about the function?
2. How would you calculate the instantaneous rate of change at $x = -5$?
3. Can the average rate of change be interpreted as the slope of a secant line? Why?
4. What happens to the average rate of change if the interval changes from $[-8, -3]$ to $[-8, -5]$?
5. How do you use this method to estimate the behavior of a function that’s not graphed?

Tip: The average rate of change between two points is essentially the slope of the straight line that connects those points on the graph.