function notation

[mathsbrain]

Hi,

A bit confused with the use of the notation y=f(x). If we have the circle x^2+y^2=1, we can obviously rearrange and make y the subject which gives y=+-(1-x^2)^0.5. Is it wrong to write f(x)=+-(1-x^2)^0.5 since this is not a function hence we can't use f(x)?
If so, does that also mean whenever we are given f(x)=..., we can assume the given relation must be a function?

[fan96]

is not a function. It is not correct to write it as one.

The function notation should only be used with functions.

[HeroWise]

THere is an imaginary vertical line test to prove if a graph is a function or not