Over the specified interval, the average rate of change is 2/3.
Finding the difference between the function values and dividing it by the difference between the corresponding x-values yields the average rate of change of a function on an interval.
The interval in this instance is -3 ≤ x ≤ 6. We must ascertain the change in y-values and the change in x-values during this time in order to calculate the average rate of change.
With these variables in hand, we can calculate the average rate of change by dividing the change in y by the change in x.
We can observe from the function's provided graph that, when x = -3, f(x) starts at a value of 1 and finishes at a value of 7. Consequently, 7 - 1 = 6 represents the shift in y-values. The x-value shift is 6 - (-3) = 9. We can now compute the mean rate of change:
Change in y: 7 - 1 = 6
Change in x: 6 - (-3) = 9
Average rate of change: 6/9 = 2/3
The probable question may be: "The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −3≤x≤6?"