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To determine the average rate of change of the function \( f(x) \) from \( x = 2 \) to \( x = 4 \), we use the following formula for the average rate of change:

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

where \( x_1 = 2 \) and \( x_2 = 4 \).

From the graph:
- At \( x = 2 \), the corresponding value of \( f(2) \) is approximately \( 4 \).
- At \( x = 4 \), the corresponding value of \( f(4) \) is approximately \( -2 \).

Now, we substitute these values into the formula:

\[
\text{Average rate of change} = \frac{f(4) - f(2)}{4 - 2} = \frac{-2 - 4}{4 - 2} = \frac{-6}{2} = -3
\]

Thus, the average rate of change of \( f(x) \) from \( x = 2 \) to \( x = 4 \) is \( -3 \).

Would you like further clarification on this? 

Here are five related questions you could explore:
1. What is the geometric interpretation of the average rate of change on the graph?
2. How would the average rate of change differ if the interval was from \( x = 1 \) to \( x = 3 \)?
3. Can the average rate of change be interpreted as the slope of the secant line between two points on a curve?
4. How does the average rate of change compare to the instantaneous rate of change?
5. What happens to the average rate of change if \( f(x) \) is a linear function?

**Tip:** The average rate of change between two points on a graph is the same as the slope of the straight line (secant line) connecting those two points.

Given the graph of f(x) below. Determine the average rate of change of f(x) from x = 2 to x = 4.

Learn how to determine the average rate of change of a function f(x) from x = 2 to x = 4 using the graph. This example covers key concepts like the slope of a secant line and the formula for average rate of change. Suitable for students in Grades 9-11.

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