A freaky function of circle

Snowboarder · #1 $Old$ 07-31-2008, 05:46 AM

Hi everyone.
So i have the curve (x^2 - 1)^2 + (y^2 - 1)^2 = 1

My question is: Why can "y" not be written as a function of x? I need to shall this somehow.
Thx for any help.

angel.white · #2 $Old$ 07-31-2008, 06:13 AM

Quote:

Originally Posted by Snowboarder $View Post$

Hi everyone.
So i have the curve (x^2 - 1)^2 + (y^2 - 1)^2 = 1

My question is: Why can "y" not be written as a function of x? I need to shall this somehow.
Thx for any help.

A function must have only one output for a given input, but in this equation there is more than one value of y per value of x.

for example this equation is satisfied for the points $(1,\sqrt{2})$ and $(1,-\sqrt{2})$ and $(1,0)$

That is three different values of y which satisfy this equation for a single value of x. Thus y cannot be a function of x.