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, 71≤x≤7.
To find the average rate of change of the function over the interval 1 ≤ x ≤ 7, we first need to find the change in the function's value over that interval.
We are given the function defined in the table below:
x | f(x)
1 | -3
5 | 9
7 | 15
To find the change in the function's value over the interval 1 ≤ x ≤ 7, we need to find the difference between the function's value at x = 7 and x = 1:
f(7) - f(1) = 15 - (-3) = 18
Next, we need to find the change in x over the same interval:
7 - 1 = 6
Now, we can find the average rate of change by dividing the change in the function's value by the change in x:
Average rate of change = (f(7) - f(1)) / (7 - 1) = 18 / 6 = 3
Therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 7 is 3.