Question

A function is given.
f(z) = 3 − 4z square; z = −2, z = 0
(a) Determine the net change between the given values of the variable.


(b) Determine the average rate of change between the given values of the variable.

Answer 1

To find the net change between the given values of the variable, we need to evaluate the function at those values and subtract the smaller value from the larger value.

For z = -2, we have:
f(-2) = 3 - 4*(-2)^2
f(-2) = 3 - 4*(4)
f(-2) = 3 - 16
f(-2) = -13

For z = 0, we have:
f(0) = 3 - 4*0^2
f(0) = 3 - 4*0
f(0) = 3 - 0
f(0) = 3

Therefore, the net change between the given values of the variable is:
-13 - 3 = -16

To find the average rate of change between the given values of the variable, we need to calculate the difference in the function values and divide by the difference in the variable values.

The difference in the function values is:
f(0) - f(-2) = 3 - (-13) = 3 + 13 = 16

The difference in the variable values is:
0 - (-2) = 0 + 2 = 2

Therefore, the average rate of change between the given values of the variable is:
16/2 = 8