Question

The area of a square is a function of its perimeter. Graph the function on a separate sheet of grid paper . Explain wether the function is linear and if the graph is increasing or decreasing .

How do i graph it ? and is the the function linear . Is the graph increasing or decreasing ? PLEASE HELP .

Answer 1

Parabola
`P^(2)` = 16A

Non-linear function.

Increasing function.

Explanation:

Let a be the side length of a square ,

Then, Perimeter of square (P) = 4a

So, a can be written as a =
`(P)/(4)`

Area of square (A) =
`a^(2)` .

So, A =
`(P^(2) )/(4^(2) )`

=
`(P^(2) )/(16 )`

`P^(2)` = 16A

It is the equation of parabola. (similar to
`y^(2)` = 4ax)

It is a non - linear function as square of Perimeter is related to Area , not directly Perimeter.

Also, it is a increasing function since as A increases P increases.