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The question in the image asks for the **average rate of change** of the function \( f(x) \) from \( x = 2 \) to \( x = 5 \), based on the graph provided.

To calculate the average rate of change of a function between two points, we use the formula:

\[
\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

Here:
- \( x_1 = 2 \)
- \( x_2 = 5 \)

From the graph, we need to determine the values of \( f(2) \) and \( f(5) \):
- At \( x = 2 \), the value of the function \( f(2) \) appears to be 4.
- At \( x = 5 \), the value of the function \( f(5) \) appears to be 2.

Now, apply these values to the formula:

\[
\text{Average rate of change} = \frac{f(5) - f(2)}{5 - 2} = \frac{2 - 4}{5 - 2} = \frac{-2}{3} \approx -0.67
\]

The correct answer is approximately **-0.67**, but it seems the provided answer was positive 0.67, which is incorrect since the slope is negative.

Would you like further details or have any additional questions?

Here are 5 related questions to expand on this concept:
1. How is the average rate of change related to the slope of a line?
2. Can the average rate of change be zero, and under what conditions?
3. What is the physical interpretation of the average rate of change in real-life applications?
4. How would you find the instantaneous rate of change at a point from a graph?
5. What happens to the rate of change as the interval between the two points becomes smaller?

**Tip:** Always check the sign of the rate of change based on the direction of the graph! A downward slope means a negative rate of change.

Use the graph of f(x) to evaluate the average rate of change of f from x = 2 to x = 5.

Learn how to calculate the average rate of change for a function between two points using the formula (f(x2) - f(x1)) / (x2 - x1). This problem covers key concepts such as slopes, functions, and graph analysis, suitable for students in Grades 9-12.

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