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To find the **average rate of change** of the function \( f(x) \) from \( x = 0 \) to \( x = 2 \), we can use the following formula:

\[
\text{Average Rate of Change} = \frac{f(2) - f(0)}{2 - 0}
\]

Now, using the graph:

- From the graph, \( f(0) = 5 \) (the y-coordinate when \( x = 0 \)).
- From the graph, \( f(2) = 0 \) (the y-coordinate when \( x = 2 \)).

Substitute these values into the formula:

\[
\text{Average Rate of Change} = \frac{0 - 5}{2 - 0} = \frac{-5}{2}
\]

Thus, the average rate of change of \( f \) from \( x = 0 \) to \( x = 2 \) is **\( \frac{-5}{2} \)** or \( -2.5 \).

Would you like more details or have any questions?

Here are some related questions you can explore:
1. What is the average rate of change of \( f(x) \) from \( x = 2 \) to \( x = 4 \)?
2. How is the average rate of change different from the instantaneous rate of change?
3. Can you find the slope of the line segment between \( x = 4 \) and \( x = 5 \)?
4. How does the graph indicate a positive or negative rate of change?
5. What is the significance of a zero slope on a graph?

**Tip:** The average rate of change is essentially the slope of the secant line between two points on the graph.

Use the graph of f(x) to evaluate the following: The average rate of change of f from x = 0 to x = 2. Give your answer as an integer or reduced fraction.

Find the average rate of change of the function f(x) from x=0 to x=2 using the graph. The solution involves applying the slope formula and interpreting points on the graph.

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