What is the average rate of change of g(x) = [3 | 2 – x | –6] over the interval of [-4, 0]?

The average rate of change of g(x) is -3 over the interval of [-4, 0].

Step-by-step explanation:

The  average rate of change  of g(x) over an interval between 2 points (a ,g(a)) and (b ,g(b)) is the slope of the  secant line  connecting the 2 points.

To calculate the average rate of change between the 2 points we use:

(g(b) - g(a)) / (b - a)

then

b = 0

a = - 4

g(b) = g(0) = 3 | 2 – 0 | – 6 = 0

g(a) = g(-4) = 3 | 2 – (– 4) | – 6 = 12

finally we get

(g(b) - g(a)) / (b-a) = (0 - 12) / (0 - (-4)) = -3

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Step-by-step explanation:

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