Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2, is less than or equal to, x, is less than or equal to, 82≤x≤8.
xx f, of, xf(x)
22 4242
44 2222
66 1010
88 66
1010 1010
1212 2222
The average rate of change of a function over an interval is the difference in the function values divided by the difference in the corresponding x-values.
We need to find the difference in the function values and the difference in the x-values for the interval 2≤x≤8.
The function values for x=2 and x=8 are f(2)=42 and f(8)=66, respectively.
The difference in the function values is 66-42=24.
The difference in the x-values is 8-2=6.
Therefore, the average rate of change of the function over the interval 2≤x≤8 is 24/6=4.