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