Question

Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3? Select one: a. f(x), g(x), h(x) b. g(x), f(x), h(x) c. h(x), g(x), f(x) d. g(x), h(x), f(x)

Answer 1

Explanation:

To find the order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3, we need to calculate the average rate of change of each function over that interval and compare them.

For f(x), we have:

average rate of change = [f(3) - f(-1)] / (3 - (-1))

= [(3+3)^2 - 2 - ((-1)+3)^2 + 2] / 4

= 23

For g(x), we have:

average rate of change = [g(3) - g(-1)] / (3 - (-1))

= [0 - (-3/2)] / 4

= 3/8

For h(x), we have:

average rate of change = [h(3) - h(-1)] / (3 - (-1))

= [(62-14)/(3-(-1))]

= 12

Therefore, the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3 is:

g(x), f(x), h(x)

So the answer is option (b).