152k views
0 votes
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

User Barin
by
7.8k points

1 Answer

5 votes

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.

User EPharaoh
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories