Consider the graph of f shown below.

Estimate the average rate of change from 
x = 2
 to 
x = 5.



To estimate the average rate of change of a function \( f(x) \) between two points \( x = 2 \) and \( x = 5 \), we use the formula:

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

Here, we need the values of \( f(2) \) and \( f(5) \), which can be estimated from the graph. Could you upload an image of the graph for a more precise calculation?

Would you like more details or have any questions so far?

### Relative questions:
1. What is the interpretation of the average rate of change in real-world applications?
2. How does the average rate of change relate to the derivative of a function?
3. Can you explain the significance of a positive vs. negative average rate of change?
4. How would we find the average rate of change for a non-linear function like a parabola?
5. How does the average rate of change compare to the instantaneous rate of change?

### Tip:
When interpreting graphs, ensure to estimate the function values at the given points accurately, especially for hand-drawn or approximate graphs.

Consider the graph of f shown below. Estimate the average rate of change from x = 2 to x = 5.

Learn how to estimate the average rate of change of a function between two points, x = 2 and x = 5, by using the slope formula on a graph. This problem introduces key concepts of rate of change and secant lines, suitable for students in Grades 9-11.

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