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The image shows a question asking for the **average rate of change** of a function \( f(x) \) from \( x = 1 \) to \( x = 3 \) using a given graph. 

To calculate the average rate of change of \( f(x) \) over the interval \([x_1, x_2]\), we use the formula:

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

### Step-by-step Solution:

1. **Identify Points on the Graph:**
   - Find \( f(1) \) and \( f(3) \) from the graph.

2. **Calculate Values from the Graph:**
   - At \( x = 1 \), the function value \( f(1) = 2 \).
   - At \( x = 3 \), the function value \( f(3) = 6 \).

3. **Apply the Formula:**
   \[
   \text{Average Rate of Change} = \frac{f(3) - f(1)}{3 - 1} = \frac{6 - 2}{2} = \frac{4}{2} = 2
   \]

Therefore, the average rate of change of \( f(x) \) from \( x = 1 \) to \( x = 3 \) is **2**.

Would you like more details, or do you have any questions?

### Further Questions to Explore:
1. How do you find the rate of change for a nonlinear function?
2. What does the average rate of change represent in a real-world context?
3. How is the average rate of change different from the instantaneous rate of change?
4. How can you interpret the slope of a line in terms of rate of change?
5. How do you calculate the average rate of change for other intervals?

### Tip:
For linear functions, the average rate of change is constant and equal to the slope of the line.

Find the average rate of change of the function f(x) from x = 1 to x = 3 based on the given graph.

Learn how to find the average rate of change of a function f(x) from x = 1 to x = 3 by using the formula (f(x2) - f(x1)) / (x2 - x1). This problem is ideal for students in Grades 9-11 and covers key algebraic concepts related to rates of change and functions.

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