Final answer:
The average rate of change between -3 and 1 of the function f(x) = -2x² + 3 is 4.
Step-by-step explanation:
The average rate of change of a function between two points can be found by calculating the difference in the function values at the two points and dividing it by the difference in the input values.
In this case, we need to find the average rate of change of the function f(x) = -2x² + 3 between x = -3 and x = 1.
First, we calculate the function value at x = -3: f(-3) = -2(-3)² + 3 = -18 + 3 = -15.
Then, we calculate the function value at x = 1: f(1) = -2(1)² + 3 = -2 + 3 = 1.
The difference in function values is: 1 - (-15) = 16.
The difference in input values is: 1 - (-3) = 4.
Finally, we divide the difference in function values by the difference in input values: average rate of change = 16/4 = 4.
Therefore, the average rate of change between x = -3 and x = 1 of the function f(x) = -2x² + 3 is 4.