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

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

From the graph:

• At $x = 1$, $f(1) = 1$.
• At $x = 3$, $f(3) = 5$.

Now, substituting these values into the formula:

$\text{Average rate of change} = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2$

Thus, the average rate of change of $f$ from $x = 1$ to $x = 3$ is $2$.

Would you like further details or have any questions?

Here are five related questions you might find helpful:

1. How is the average rate of change related to the slope of a line?
2. What does the sign of the average rate of change indicate about the function's behavior?
3. How would the average rate of change differ if calculated over a different interval, such as $x = 0$ to $x = 4$?
4. Can the average rate of change be negative? If so, under what conditions?
5. What is the significance of the average rate of change in real-world applications?

Tip: The average rate of change formula is very similar to the slope formula for a straight line, so always check the coordinates carefully.