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?

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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