# How do find if a relation is a function algebraically

Is there a way to see if a relation is a function without having to do a "vertical line test" (where you draw a vertical line on the graph and if there line touches two points then it's not a function).

To determine if a function is even or odd you simply go f(x) = f(-x); even, f(-x) = -f(x); odd. Can I do something similar to find out if a relation is a function?

Thanks

• Your example of even and odd functions isn't really an algebraic way of solving. – Simply Beautiful Art Feb 17 '16 at 23:06
• Ok, what type of method is it? – frog1944 Feb 17 '16 at 23:09
• I don't know. But that's definitely not 'solved' algebraically, I can tell you that much. – Simply Beautiful Art Feb 17 '16 at 23:10
• Ok, thanks @Simple Art. – frog1944 Feb 17 '16 at 23:12

• @frog1944 Well, you can break it up into parts and pieces if that makes it easier. Also look to see if it is defined for all $x$, else it isn't a relation. And of course, this depends on if you consider $x\in\mathbb{R}$ or something different. But no, not that I think. – Simply Beautiful Art Feb 17 '16 at 23:11