Calculate the average rate of change over the interval [−1,1] using the given graph of the function.
The average rate of change is
The average rate of change is equal to the change in the y-values divided by the change in the x-values.
In this case, the change in the y-values is equal to the difference in the function values at the endpoints of the interval: f(1) - f(-1).
The change in the x-values is equal to the difference in the x-coordinates of the endpoints of the interval: 1 - (-1) = 2.
Therefore, the average rate of change over the interval [-1, 1] is (f(1) - f(-1))/2.