Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 18, is less than or equal to, x, is less than or equal to, 2418≤x≤24.
xx	f, of, xf(x)
1212	4141
1818	4040
2424	3939
3030	3838


The average rate of change of a function over an interval \([x_1, x_2]\) is given by the formula:

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

In this case, the interval is \( 18 \leq x \leq 24 \), so \( x_1 = 18 \) and \( x_2 = 24 \). From the table:

- \( f(18) = 40 \)
- \( f(24) = 39 \)

Now, applying the formula:

\[
\text{Average rate of change} = \frac{f(24) - f(18)}{24 - 18} = \frac{39 - 40}{24 - 18} = \frac{-1}{6}
\]

So, the average rate of change of the function over the interval \( 18 \leq x \leq 24 \) is \( \frac{-1}{6} \).

Would you like further details or have any questions about this?

Here are 5 related questions to explore:

1. How does the average rate of change compare to the slope of a linear function?
2. What does a negative average rate of change indicate about the function's behavior?
3. How would the average rate of change differ over a larger interval?
4. Can we interpret the function as decreasing consistently based on the values in the table?
5. How is the average rate of change connected to the concept of a derivative?

**Tip:** The average rate of change is essentially the slope of the secant line connecting two points on the graph of the function!

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 18 ≤ x ≤ 24.

x    f(x)
12   41
18   40
24   39
30   38

Learn how to calculate the average rate of change of a function over the interval 18 ≤ x ≤ 24. The table values of the function are provided, and the formula for the average rate of change is applied step-by-step. This is ideal for high school students covering algebra and functions.

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