Compare the functions shown below:

f(x)

x y

−3 −27

−2 −8

−1 −1

0 0

1 1

2 8

3 27

4 64

g(x)

linear graph with y intercept of negative 1 and x intercept of negative 2 h(x) = (x + 4)2 + 2

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4?

f(x)

x y

−3 −27

−2 −8

−1 −1

0 0

1 1

2 8

3 27

4 64

g(x)

linear graph with y intercept of negative 1 and x intercept of negative 2 h(x) = (x + 4)2 + 2

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4?

To get the average rate of change, we simply have to use this formula:

ARC = (y2 -y1) / (x2 - x1)

For the first function:

ARC = (64 - 0) / (4 - 0) = 16

For the second function, since it’s a line, the ARC would just be equal to the slope

m = ARC = (-1 - 0) / (0 - (-2)) = -0.5

For the third function:

h(0) = 18

h(4) = 66

ARC = (66 - 18) / (4 - 0) = 12

Therefore, the order of the functions from lest to greatest according to the average rate of change on the interval from x= 0 to x = 4 is:

g(x)

h(x)

f(x)

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