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, 5, is less than or equal to, x, is less than or equal to, 4−5≤x≤4?
To find the average rate of change of the function f(x) on the interval [-5, 4], we need to calculate the change in y divided by the change in x.
Let's denote the function f(x) as y and let the points on the graph where x = -5 have coordinates (-5, f(-5)) and where x = 4 have coordinates (4, f(4)).
The change in y is f(4) - f(-5) and the change in x is 4 - (-5) = 9.
Therefore, the average rate of change of f(x) on the interval [-5, 4] is:
Avg rate of change = (f(4) - f(-5)) / (4 - (-5)) = (f(4) - f(-5))/9.