Final answer:
The average rate of change of the function h(x) = x^2 - 1 over the interval -3 < x < -1 is -4, which is option A.
Step-by-step explanation:
To find the average rate of change of the function h(x) = x^2 - 1 over the interval -3 < x < -1, we will first evaluate the function at the endpoints of the interval. The average rate of change is given by the formula:
Average Rate of Change = (h(x2) - h(x1)) / (x2 - x1)
Where x1 is -3 and x2 is -1. Evaluating the function at these points gives us:
- h(-3) = (-3)^2 - 1 = 9 - 1 = 8
- h(-1) = (-1)^2 - 1 = 1 - 1 = 0
Now, we plug these values into the average rate of change formula:
(0 - 8) / (-1 - (-3)) = (-8) / (2) = -4
Therefore, the average rate of change of the function h(x) over the interval -3 < x < -1 is -4.