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, 3618≤x≤36.
xx f, of, xf(x)
00 1313
99 2525
1818 3737
2727 4949
3636 6161
The average rate of change of a function over an interval can be found by taking the difference in function values and dividing by the difference in input values. In this case, we are looking for the average rate of change of f(x) over the interval 18 ≤ x ≤ 36.
The difference in function values is 6161 - 1313 = 4848.
The difference in input values is 3636 - 0 = 3636.
Therefore, the average rate of change is 4848/3636 = 4/3.
So, the average rate of change of the function over the interval 18 ≤ x ≤ 36 is 4/3.