To determine the average rate of change of $f(x)$ between $x = -3$ and $x = 2$, we will use the formula for the average rate of change of a function over an interval:

$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

Here:

• $x_1 = -3$
• $x_2 = 2$

From the graph, we need to estimate the values of $f(x_1)$ and $f(x_2)$:

• When $x = -3$, it appears that $f(-3) \approx 4$.
• When $x = 2$, it appears that $f(2) \approx -2$.

Now we can plug these values into the formula:

$\text{Average Rate of Change} = \frac{f(2) - f(-3)}{2 - (-3)} = \frac{-2 - 4}{2 + 3} = \frac{-6}{5}$

Thus, the average rate of change is $\frac{-6}{5}$.

Would you like any further details or explanations on this?

Here are 5 related questions:

1. What does the average rate of change tell us about the behavior of the function on this interval?
2. How is the average rate of change similar to the slope of a secant line?
3. Can the average rate of change be positive for some intervals on this graph?
4. How would you compute the average rate of change if the function were given algebraically?
5. What is the difference between the average rate of change and the instantaneous rate of change?

Tip: When finding the average rate of change from a graph, carefully estimate the coordinates of the points involved to avoid errors.