Question

Given the function f(x) = –22 + 4x + 9, determine the average rate of change of the function over the interval 1 < x < 7. Which of the following options correctly represents the average rate of change?

A) 4
B) 6
C) 8
D) 10

Answer 1

The average rate of change of the function f(x) = –22 + 4x + 9 over the interval 1 < x < 7 is calculated by taking the difference of f(x) at x = 7 and x = 1, then dividing by 6. The result is 4, making option A) 4 the correct answer.

Step-by-step explanation:

To determine the average rate of change of the function f(x) = –22 + 4x + 9 over the interval 1 < x < 7, we need to calculate the change in the function's value over this interval and then divide by the change in x. We do this by subtracting the value of f(x) at x = 1 from the value of f(x) at x = 7, and then dividing by the change in x which is 7 - 1.

• First, calculate f(7): f(7) = –22 + 4(7) + 9 = –22 + 28 + 9 = 15.
• Next, calculate f(1): f(1) = –22 + 4(1) + 9 = –22 + 4 + 9 = –9.
• The change in f(x) is 15 - (–9) = 24.
• The change in x is 7 - 1 = 6.
• Finally, divide the change in function values by the change in x: 24 / 6 = 4.

Therefore, the correct option for the average rate of change of the function over the given interval is A) 4.