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
Answer
Attempt 1 out of 2
To find the average rate of change of the function over the interval 2 ≤ x ≤ 8, we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.
The function values at the endpoints of the interval are f(2) = 42 and f(8) = 66.
The difference in the function values is 66 - 42 = 24.
The difference in the x-values is 8 - 2 = 6.
The average rate of change is 24/6 = 4.
Therefore, the average rate of change of the function over the interval 2 ≤ x ≤ 8 is 4.