The average rate of change of a function between points (a, b) and (c, d) on the graph of the function is given by:
rate of change = (d - b)/(c - a)
For this problem, we have the function g(x) = -3x² - 1, and we want to find the average rate of change between two points on the graph of the function, which are:
(-3, -28) and (3, -28)
Notice that both points belong indeed to the graph of g(x) since
-3(±3)² - 1 = -3 * 9 - 1 = -27 - 1 = 28
So, to find the average rate of change between those points, we can use the above definition with
a = -3
b = -28
c = 3
d = -28
Then, the average rate of change is given by:
rate of change = [-28 - (-28)]/[3 - (-3)] = (-28 + 28)/(3 +3) = 0
Therefore, the average rate of change is 0.