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The question asks for the **average rate of change** of the function \( f(x) \) on the interval \( 1 \leq x \leq 3 \). 

The average rate of change of a function over an interval \([a, b]\) is calculated using the formula:
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]
Here, the interval is \( 1 \leq x \leq 3 \), so \( a = 1 \) and \( b = 3 \).

From the graph:
- The value of \( f(1) \) appears to be approximately \( -8 \).
- The value of \( f(3) \) appears to be approximately \( 6 \).

Now we can calculate the average rate of change:
\[
\frac{f(3) - f(1)}{3 - 1} = \frac{6 - (-8)}{3 - 1} = \frac{6 + 8}{2} = \frac{14}{2} = 7
\]

Thus, the **average rate of change** is \( 7 \).

Would you like more details, or have any questions about this?

### Related Questions:
1. How do you interpret the average rate of change in real-life scenarios?
2. How does the average rate of change differ from the instantaneous rate of change?
3. What are the characteristics of functions with a constant average rate of change?
4. How would the average rate of change change if the interval were \( 1 \leq x \leq 5 \)?
5. How can you determine concavity or inflection points from the rate of change?

### Tip:
To estimate values from a graph more accurately, try identifying key points or using graphing software to enhance precision.

The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1 ≤ x ≤ 3?

Learn how to calculate the average rate of change of the function f(x) using the graph on the interval 1 ≤ x ≤ 3. This problem covers key algebraic concepts like functions and the formula for average rate of change. Suitable for students in Grades 9-12.

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