Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3, is less than or equal to, x, is less than or equal to, 3≤x≤5.
xx f, of, xf(x)
1 80
2 73
3 66
4 59
5 52
The average rate of change of the function over the interval 3 ≤ x ≤ 5 can be found by taking the change in the function values over the interval and dividing by the change in the input values:
Average rate of change = (f(5) - f(3)) / (5 - 3)
First, we find the values of the function at x=3 and x=5:
f(3) = 66
f(5) = 52
Now, we plug these values into the formula:
Average rate of change = (52 - 66) / (5 - 3)
Average rate of change = -14 / 2
Average rate of change = -7
Therefore, the average rate of change of the function over the interval 3 ≤ x ≤ 5 is -7.