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Given the graph of the function f(x) shown below, find the average rate of change of the function f(x) on the interval [5,20].

To find the average rate of change of the function \( f(x) \) over the interval \([5, 20]\), we use the formula:

\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = 5 \) and \( b = 20 \). So, we need to determine the values of \( f(5) \) and \( f(20) \) from the graph.

1. From the graph, \( f(5) \) appears to be around \( f(5) \approx 15 \).
2. Similarly, \( f(20) \) appears to be around \( f(20) \approx 35 \).

Now, applying the formula:

\[
\text{Average rate of change} = \frac{f(20) - f(5)}{20 - 5} = \frac{35 - 15}{15} = \frac{20}{15} = \frac{4}{3}
\]

Thus, the average rate of change of \( f(x) \) over the interval \([5, 20]\) is \( \frac{4}{3} \) units per unit change in \( x \).

Would you like further clarification or details? 

Here are 5 questions related to this topic:
1. How is the average rate of change different from the instantaneous rate of change?
2. What does the average rate of change tell us about the behavior of the function on a given interval?
3. How do you interpret the sign of the average rate of change in terms of the function's graph?
4. Can the average rate of change be negative? Under what conditions?
5. How can we calculate the instantaneous rate of change at a specific point on a curve?

**Tip:** The average rate of change of a function over an interval gives the slope of the secant line connecting two points on the curve within that interval.

Given the graph of the function f(x) shown below, find the average rate of change of the function f(x) on the interval [5,20].

Learn how to find the average rate of change of the function f(x) on the interval [5, 20] using the formula for rate of change. The problem involves interpreting values from the graph and applying the formula. Suitable for students in Grades 9-12.

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