Final answer:
The average rate of change over the interval [-2, -1] is -3. The average rate of change is calculated using the slope of the secant line is -3.
Step-by-step explanation:
The average rate of change of a function over an interval is the slope of the line connecting the two points on the graph of the function corresponding to the endpoints of the interval. To calculate the average rate of change over the interval [-2, -1], you need to find the difference in the function values at the endpoints divided by the difference in the x-coordinates.
Let's assume the function is f(x) = x^2. Evaluating the function at x = -2 and x = -1, we have f(-2) = (-2)^2 = 4 and f(-1) = (-1)^2 = 1. The difference in the function values is 4 - 1 = 3, and the difference in the x-coordinates is -2 - (-1) = -1. Therefore, the average rate of change over the interval [-2, -1] is 3 / (-1) = -3.