Question

calculate the average rate of change over the interval [-1,3] for the function show your work in a 9th grade explanation don't make it to obvious that you wrote it

f(x) = x^2 + 2x - 2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2, we need to find the change in the function's value over that interval and then divide it by the change in the input values.

First, we need to find the function values at the endpoints of the interval:
f(-1) = (-1)^2 + 2(-1) - 2 = 1 - 2 - 2 = -3
f(3) = (3)^2 + 2(3) - 2 = 9 + 6 - 2 = 13

Next, we calculate the change in the function values:
Change in function values = f(3) - f(-1) = 13 - (-3) = 16

Then, we find the change in the input values:
Change in input values = 3 - (-1) = 3 + 1 = 4

Finally, we calculate the average rate of change by dividing the change in function values by the change in input values:
Average rate of change = Change in function values / Change in input values = 16 / 4 = 4

Therefore, the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2 is 4.