Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 1, is less than or equal to, x, is less than or equal to, 1≤x≤5.
xx f, of, xf(x)
1 47
2 37
3 27
4 17
5 7
The average rate of change of a function over an interval is given by the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
Where a and b are the endpoints of the interval.
In this case, the interval is 1 ≤ x ≤ 5, so a = 1 and b = 5. The values of the function at a and b are f(1) = 47 and f(5) = 7, respectively.
Average Rate of Change = (f(5) - f(1)) / (5 - 1) = (7 - 47) / 4 = -40 / 4 = -10
Therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 5 is -10.