Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 6, is less than or equal to, x, is less than or equal to, 306≤x≤30.
xx f, of, xf(x)
00 77
66 1616
1212 2525
1818 3434
2424 4343
3030 5252
To find the average rate of change of the function over the given interval, we need to calculate the difference in the y-values divided by the difference in the x-values.
For the interval 6 ≤ x ≤ 30, the difference in the x-values is: 30 - 6 = 24.
The difference in the y-values is: f(30) - f(6) = 5252 - 16 = 5236.
Therefore, the average rate of change is: 5236/24 = 219/1 = 219.