How do I ascertain whether an equation defines a function? Asides from graphing an equation are there any other ways of determining if an equation is a function?

If you can re-write the equation as a dependent variable and a independent variable, so Y = an equation only involving X, then verify that each X determines only 1 value for Y (i.e, there are no $\pm$ or you don't need to take even roots of Y to isolate it etc.)