Indentify Functions Y^2=X

Question

I need to know if the equation y^2=x a function or a relation. I also need to know if it’s neither or both two.

Answer 1

As a set of ordered pairs it is a relation.

It is not a function since for every input there exists two outputs.

E.G. if x = 4 y could be ±2

Graph it and it fails the vertical line test.

Answer 2

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

x = y^2

You can see from this equation that, for example, if x = 4, then y could equal 2 or -2. Therefore, not a function. x can be associated with only one y.