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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.

Use the graph of the function to find its average rate of change from x = -9 to x = -5.

Learn how to calculate the average rate of change from the graph of a function between x = -9 and x = -5. This example focuses on interpreting the graph and applying the average rate of change formula. Ideal for high school algebra students.

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