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.