Question

calculate the average rate of change over the interval [-1,3] for the function show your work in a 8th 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 find the average rate of change of the function over the interval [-1,3], we first need to calculate the value of the function at x=-1 and x=3.

When x = -1:
f(-1) = (-1)^2 + 2(-1) - 2
f(-1) = 1 - 2 - 2
f(-1) = -3

When x = 3:
f(3) = (3)^2 + 2(3) - 2
f(3) = 9 + 6 - 2
f(3) = 13

Next, we can calculate the average rate of change over the interval [-1,3] using the formula:
Average Rate of Change = (f(3) - f(-1)) / (3 - (-1))

Plugging in the values:
Average Rate of Change = (13 - (-3)) / (3 - (-1))
Average Rate of Change = (13 + 3) / (3 + 1)
Average Rate of Change = 16 / 4
Average Rate of Change = 4

Therefore, the average rate of change of the function over the interval [-1,3] is 4.