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
We can find the average rate of change of the function over the interval by taking the difference in function values and dividing by the difference in x-values.
The average rate of change between x=2 and x=8 is:
$\frac{f(8) - f(2)}{8 - 2} = \frac{6-42}{6} = \boxed{-6}.$