Determine the net change and average rate of change between the values of the variable

Question

A function is given.
f(z) = 3 − 4z²; 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

Hi K,

 

Before we can calculate the net change or average rate of change, we should calculate the values of f(-2) and f(0).

 

Since f(z) = 3 - 4z^2

 

f(-2) = 3 - 4(-2)^2

= 3 -  4(4)

= 3 - 16

=-13

 

f(0) = 3 - 4(0)^2

= 3 - 4(0)

= 3 - 0

= 3

 

The net change is simply the difference f(0) - f(-2) = 3 - (-13) = 3 + 13 = 16

The average rate of change takes the net change and divides it by the change in the x value.  In other words, it would be the slope of line through (-2, -13) and (0, 3)

 

So, that equals 16/2 which is 8.

 

Hope this helps.

:)

 

 

Answer 2

f(0) = 3 - 4(0)^2 = 3 - 4(0) = 3 - 0 = 3

 

f(-2) = 3 - 4(-2)^2 = 3 - 4(4) = 3 - 16 = -13

 

change in independent variable:  0 - (-2) = 0 + 2 = 2

 

change in dependent variable:  f(0) - f(-2) = 3 - -13 = 3 + 13 = 16

 

Average change or slope is  [ f(0) - f(-2) ] / ( 0 - -2) = 16/2 = 8