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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.

What is the average rate of change of the function f(x) on the interval −8 ≤ x ≤ −3?

Find the average rate of change of the function f(x) between x = −8 and x = −3. This problem involves calculating the slope of the secant line, a key concept in understanding the behavior of functions. Suitable for students in Grades 10-12.

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