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

Answer:

Parabola $P^{2}$ = 16A

Non-linear function.

Increasing function.

Step-by-step explanation:

Let a be the side length of a square ,

Then, Perimeter of square (P) = 4a

So, a can be written as a = $\frac{P}{4}$

Area of square (A) = $a^{2}$ .

So, A = $\frac{P^{2} }{4^{2} }$

        =  $\frac{P^{2} }{16 }$

$P^{2}$ = 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.