To find the average rate of change of the function between $x = 1$ and $x = 3$, we use the formula for the average rate of change:

$\text{Average rate of change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

where $x_1 = 1$ and $x_2 = 3$, and $f(x_1)$ and $f(x_2)$ are the corresponding function values at those points.

From the graph:

• At $x = 1$, the function $f(1) = 10$
• At $x = 3$, the function $f(3) = 40$

Now, we substitute these values into the formula:

$\text{Average rate of change} = \frac{40 - 10}{3 - 1} = \frac{30}{2} = 15$

Thus, the average rate of change is 15.

Would you like further details or have any questions?

Here are 5 related questions:

1. How does the average rate of change relate to the slope of a line?
2. What does the average rate of change tell us about the function's behavior between two points?
3. How do you calculate the instantaneous rate of change for a nonlinear function?
4. How can you interpret the rate of change in real-world problems?
5. What is the difference between the average and instantaneous rates of change?

Tip: The average rate of change of a function between two points is similar to finding the slope of the secant line through those points.