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

$\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

Here:

• $x_1 = 1$ and $x_2 = 3$
• From the graph:
  • $f(1) = 2$
  • $f(3) = 5$

Substitute these values into the formula:

$\text{Average Rate of Change} = \frac{f(3) - f(1)}{3 - 1} = \frac{5 - 2}{3 - 1} = \frac{3}{2} = 1.5$

Final Answer:

The average rate of change of $f$ from 1 to 3 is 1.5.

Would you like further explanation or details? Here are 5 follow-up questions for further exploration:

1. What does the average rate of change represent in practical terms?
2. How would the average rate of change change if calculated between $x = 3$ and $x = 5$?
3. Can the average rate of change be negative? Why or why not?
4. How does the average rate of change relate to the slope of a line?
5. What is the instantaneous rate of change, and how does it differ from the average?

Tip: When interpreting graphs, always double-check the coordinates carefully to avoid errors!