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.