The average rate of change of the function f(x) on the interval -4 < x < -3 is -5. This means that the function is decreasing at an average rate of 5 units per unit change in x.
The graph shows a decreasing function between x = -4 and x = -3. To calculate the average rate of change, we can imagine drawing a secant line that intersects the graph at the interval's endpoints. The slope of this line will represent the function's average rate of change over that interval.
From the graph, we can estimate that the secant line intersects the graph at points (x, y) = (-4, 30) and (-3, 25). Therefore, the slope of the secant line is:
m = (y2 - y1) / (x2 - x1)
= (25 - 30) / (-3 - (-4))
= -5 / 1
= -5
Therefore, the average rate of change of the function f(x) on the interval -4 < x < -3 is -5. This means that for every one unit increase in x, the function's value decreases, on average, by 5 units.
In other words, the function is decreasing at a rate of 5 units per unit change in x.
The question probable 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 -4 < x < -3?