Question

Given the function defined in the table below, find the average rate of change, in simplest form,

of the function over the interval 4 ≤ x ≤ 8.
89
3
4
5
6
7
8
f(x)
3
7
13
21
31
43

Answer 1

The average rate of change of the function over the interval 4 ≤ x ≤ 8 is 5.5.

Step-by-step explanation:

The average rate of change of a function over an interval is calculated by finding the difference in function values at the end points and dividing by the length of the interval. In this case, we are interested in finding the average rate of change of f(x) over the interval 4 ≤ x ≤ 8.

To find this, we would use the values of f(x) at x=4 and x=8 from the given table, which are f(4) = 21 and f(8) = 43. The formula for average rate of change is:

Average Rate of Change = Δf(x) / Δx = (f(8) - f(4)) / (8 - 4)

Now substitute the values from the table:

Average Rate of Change = (43 - 21) / (8 - 4) = 22 / 4 = 5.5

Thus, the average rate of change of this function over the interval from x = 4 to x = 8 is 5.5.