Question

Given the function h(x) = x^2 - 1, what is the average rate of change of h over the interval -3 < x < -1?

A. -4
B. -2
C. 0
D. 2

Answer 1

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.