Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 7, is less than or equal to, x, is less than or equal to, 107≤x≤10.
xx f, of, xf(x)
11 44
44 1313
77 2222
1010 3131
1313 4040
To find the average rate of change, we need to find the difference in the y-values divided by the difference in the x-values.
Change in y-value: 4040 - 44 = 3996
Change in x-value: 1313 - 11 = 1302
Average rate of change = (Change in y-value)/(Change in x-value)
Average rate of change = 3996/1302
Simplifying the fraction, we get:
Average rate of change = 333/109