calculate the average rate of change over the interval [-1,3] for the function show your work in a 7th grade explanation don't make it to obvious that you wrote it
f(x) = x^2 + 2x - 2
To find the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2, we first need to calculate the values of the function at each endpoint of the interval.
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 find the change in the function value over the interval:
Change in function value = f(3) - f(-1)
Change in function value = 13 - (-3)
Change in function value = 16
Finally, we find the average rate of change by dividing the change in function value by the change in x-value:
Average rate of change = Change in function value / Change in x-value
Average rate of change = 16 / (3 - (-1))
Average rate of change = 16 / 4
Average rate of change = 4
Therefore, the average rate of change over the interval [-1,3] for the function f(x) = x^2 + 2x - 2 is 4.