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, 6, is less than or equal to, x, is less than or equal to, minus, 2−6≤x≤−2?
To find the average rate of change of the function f(x) on the interval -6 ≤ x ≤ -2, we need to calculate the slope of the secant line passing through the points (-6, f(-6)) and (-2, f(-2)).
Let's assume the coordinates of the points are (-6, y1) and (-2, y2).
The formula for average rate of change is given by:
Average rate of change = Δy/Δx = (y2 - y1) / (x2 - x1) = (f(-2) - f(-6)) / (-2 - (-6))
From the graph, we can see that the value of f(-6) is approximately -12 and the value of f(-2) is approximately 3.
Therefore, the average rate of change of the function f(x) on the interval -6 ≤ x ≤ -2 is:
= (3 - (-12)) / (-2 - (-6))
= (3 + 12) / 4
= 15 / 4
= 3.75
So, the average rate of change of the function f(x) on the interval -6 ≤ x ≤ -2 is 3.75.