Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0, is less than or equal to, x, is less than or equal to, 60≤*x*≤6.

x*x*f, of, x*f*(*x*)

00

99

22

1111

44

1313

66

1515

To find the average rate of change of a function over an interval, we use the formula:

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

where \(a\) and \(b\) are the endpoints of the interval, and \(f(a)\) and \(f(b)\) are the function values at those points.

### Given Data:
- Interval: \( 0 \leq x \leq 6 \)
- From the table:
  - \( f(0) = 0 \)
  - \( f(6) = 15 \)

### Applying the formula:
\[
\text{Average Rate of Change} = \frac{f(6) - f(0)}{6 - 0} = \frac{15 - 0}{6} = \frac{15}{6} = 2.5
\]

Thus, the average rate of change of the function over the interval \(0 \leq x \leq 6\) is **2.5**.

Would you like more details or have any questions? Here are five related questions for further practice:

1. What is the average rate of change between \(x = 2\) and \(x = 4\)?
2. Can you explain how the average rate of change relates to the slope of a line?
3. What happens to the average rate of change if the function values are all the same?
4. How does the average rate of change differ from instantaneous rate of change?
5. How would you calculate the average rate of change over the interval \(x = 4\) to \(x = 6\)?

**Tip:** The average rate of change over an interval gives the slope of the secant line passing through two points on the graph.

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0 ≤ x ≤ 6.

x: 0, 9, 2, 11, 4, 13, 6, 15
f(x): 0, 9, 2, 11, 4, 13, 6, 15

Learn how to calculate the average rate of change of a function over the interval 0 ≤ x ≤ 6 using the formula (f(b) - f(a)) / (b - a). This example walks you through solving the problem step-by-step, showing how f(0) = 0 and f(6) = 15 yield an average rate of change of 2.5. Suitable for students in Grades 7-9.

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