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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.

What is the average rate of change of the function from x = 1 to x = 3?

Calculate the average rate of change of a function from x = 1 to x = 3 using the formula (f(x2) - f(x1)) / (x2 - x1). This example is suitable for students in Grades 9-10, focusing on understanding functions and rates of change.

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