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To find the average rate of change of the function \( f(x) \) on the interval \( -8 \leq x \leq -6 \), we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = -8 \) and \( b = -6 \) in this case.

### Step-by-Step Solution
1. **Identify \( f(-8) \)**: From the graph, we observe that when \( x = -8 \), \( f(x) = 12 \).
2. **Identify \( f(-6) \)**: Similarly, when \( x = -6 \), \( f(x) = 18 \).
3. **Apply the formula**:

   \[
   \text{Average Rate of Change} = \frac{f(-6) - f(-8)}{-6 - (-8)}
   \]

4. **Substitute values**:

   \[
   = \frac{18 - 12}{-6 + 8} = \frac{6}{2} = 3
   \]

### Answer
The average rate of change of \( f(x) \) on the interval \( -8 \leq x \leq -6 \) is \( 3 \).

Would you like further details on this solution, or do you have any other questions?

Here are some additional related questions to explore:

1. What is the interpretation of the average rate of change in terms of slope?
2. How would the average rate of change differ if we chose a different interval?
3. Can we find the instantaneous rate of change at a specific point within this interval?
4. What would be the effect on the average rate of change if \( f(x) \) had different values at \( x = -8 \) and \( x = -6 \)?
5. How does the average rate of change relate to the behavior of the graph on the chosen interval?

**Tip**: The average rate of change over an interval gives the slope of the secant line between the two endpoints on the graph.

What is the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -6?

Calculate the average rate of change for the function f(x) on the interval -8 ≤ x ≤ -6 using graph analysis and the rate of change formula. Perfect for students in Grades 9-12 exploring function behavior.

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