To find the average rate of change of the function $g(x)$ from $x = -9$ to $x = -5$, we use the formula for the average rate of change of a function between two points:

$\text{Average rate of change} = \frac{g(x_2) - g(x_1)}{x_2 - x_1}$

Here, $x_1 = -9$ and $x_2 = -5$. Based on the graph:

• At $x = -9$, $g(-9) = 6$.
• At $x = -5$, $g(-5) = -2$.

Now, applying the values to the formula:

$\text{Average rate of change} = \frac{g(-5) - g(-9)}{-5 - (-9)} = \frac{-2 - 6}{-5 + 9} = \frac{-8}{4} = -2$

Thus, the average rate of change of the function from $x = -9$ to $x = -5$ is -2.

Would you like further details on this calculation?

Here are 5 questions that extend this concept:

1. What does a negative average rate of change signify about the function?
2. How does the average rate of change compare to the instantaneous rate of change at a point?
3. Can you interpret the graph's slope between different intervals to predict behavior?
4. How would you find the average rate of change over different intervals, say from $x = -9$ to $x = -7$?
5. What is the connection between the average rate of change and the secant line on the graph?

Tip: The average rate of change is closely related to the slope of the secant line that connects two points on the graph of the function.