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To find the average rate of change of the function \( f(x) \) on the interval \([-9, 1]\), we use the formula for the average rate of change:

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

where \( a = -9 \) and \( b = 1 \).

### Step 1: Determine \( f(-9) \) and \( f(1) \)
From the graph:
- \( f(-9) = -16 \) (this is the y-value corresponding to \( x = -9 \)),
- \( f(1) = -8 \) (this is the y-value corresponding to \( x = 1 \)).

### Step 2: Apply the formula
Now, substitute these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(1) - f(-9)}{1 - (-9)} = \frac{-8 - (-16)}{1 + 9} = \frac{-8 + 16}{10} = \frac{8}{10} = 0.8
\]

### Conclusion:
The average rate of change of \( f(x) \) on the interval \([-9, 1]\) is \( 0.8 \).

Would you like further details or have any questions?

### Relative Questions:
1. How do you interpret the average rate of change of a function geometrically?
2. What does a positive average rate of change imply about the function over the given interval?
3. How is the average rate of change related to the slope of a secant line?
4. Can the average rate of change be negative? Under what conditions?
5. How does the concept of the derivative relate to the average rate of change?

### Tip:
The average rate of change between two points on a function is essentially the slope of the line connecting those two points (the secant line).

The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -9 ≤ x ≤ 1?

Find the average rate of change of the function f(x) on the interval -9 ≤ x ≤ 1 using the formula for the slope of the secant line. This problem covers key calculus concepts suitable for students in Grades 10-12.

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