The function y, equals, f, of, xy=f(x) is graphed below. What is the average rate of change of the function f, of, xf(x) on the interval minus, 8, is less than or equal to, x, is less than or equal to, minus, 6−8≤x≤−6?
To find the average rate of change of a function on an interval, we use the formula:
(Average Rate of Change) = [f(b) - f(a)] / (b - a)
In this case, our interval is from -8 to -6. So a = -8, b = -6.
Therefore, the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -6 is:
[f(-6) - f(-8)] / (-6 - (-8)) = [f(-6) - f(-8)] / 2
From the graph provided, we can see that f(-8) = 4 and f(-6) = 2.
So, the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -6 is:
[2 - 4] / 2 = -2 / 2 = -1