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To calculate the average rate of change of the function \( f(x) \) from \( x = 1 \) to \( x = 3 \), we use the formula for the average rate of change:

\[
\text{Average rate of change} = \frac{f(3) - f(1)}{3 - 1}
\]

From the graph:

- \( f(1) = -1 \)
- \( f(3) = 5 \)

Now, plug these values into the formula:

\[
\text{Average rate of change} = \frac{5 - (-1)}{3 - 1} = \frac{5 + 1}{2} = \frac{6}{2} = 3
\]

Thus, the average rate of change from \( x = 1 \) to \( x = 3 \) is **3**.

Would you like more details or have any further questions?

Here are five related questions:
1. How would the rate of change change if we used \( x = 1 \) to \( x = 4 \)?
2. What is the physical interpretation of the average rate of change in a real-world context?
3. How do you compute the instantaneous rate of change from a graph like this?
4. Can the average rate of change ever be negative? How would that look on a graph?
5. What is the relationship between the slope of a line segment and the average rate of change?

**Tip:** The average rate of change over an interval can be interpreted as the slope of the secant line connecting two points on the graph.

Use the graph of f(x) to evaluate the average rate of change of f from x = 1 to x = 3. Give your answer as an integer or reduced fraction.

Learn how to calculate the average rate of change of the function f(x) from x = 1 to x = 3 using a graph. This solution shows how to apply the formula for average rate of change, based on the slope between two points on the function graph. Suitable for students in Grades 8-10.

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