Final answer:
To determine the average rate of change of a function over an interval, find the difference in function values at the endpoints and divide it by the difference in x-values.
Step-by-step explanation:
The average rate of change of a function over an interval is determined by calculating the difference between the function values at the endpoints of the interval and dividing it by the difference between the x-values of the endpoints.
In this case, the function is g(x) = -22x^2 - 52x + 8. To determine the average rate of change over the interval -5 < x < 2, we need to find g(2) and g(-5). Plugging these values into the function, we get g(2) = -22(2)^2 - 52(2) + 8 and g(-5) = -22(-5)^2 - 52(-5) + 8.
After calculating these values, we can find the average rate of change by subtracting g(-5) from g(2) and dividing it by 2 - (-5). This gives us the average rate of change of the function over the interval -5 < x < 2.