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To find the average rate of change of the function \( f \) from \( x = -6 \) to \( x = -5 \), we can use the formula for the average rate of change:

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

where \( a = -6 \) and \( b = -5 \).

### Step 1: Determine \( f(-6) \) and \( f(-5) \) from the graph
- From the graph, the y-value corresponding to \( x = -6 \) is \( f(-6) = 9 \).
- The y-value corresponding to \( x = -5 \) is \( f(-5) = 4 \).

### Step 2: Calculate the average rate of change
\[
\text{Average rate of change} = \frac{f(-5) - f(-6)}{-5 - (-6)} = \frac{4 - 9}{-5 + 6} = \frac{-5}{1} = -5
\]

So, the average rate of change from \( x = -6 \) to \( x = -5 \) is:

\[
-5
\]

Would you like more details or have any questions?

### Related Questions
1. How do you find the average rate of change for a general interval [a, b]?
2. How does the average rate of change relate to the slope of the secant line?
3. What is the physical interpretation of the average rate of change for a real-world scenario?
4. How can you determine the rate of change from a function equation instead of a graph?
5. What would the average rate of change be for different intervals on the same graph?

### Tip
Always double-check the coordinates on a graph to ensure the accuracy of your calculations.

Use the graph of the function to find its average rate of change from x = -6 to x = -5. Simplify your answer as much as possible.

Learn how to find the average rate of change of a function using a graph, from x = -6 to x = -5. This problem focuses on key algebraic concepts, including functions and the average rate of change formula. Suitable for students in Grades 9-10.

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