Question

How do I determine whether a given relation is a function?

Answer 1

Here are a couple of methods...

Explanation:

Set of points

If the relation is expressed in terms of a small list of points, first eliminate any duplicates (that is equal `x` and `y` coordinates), then check to see if the `x` coordinates of the remaining points are distinct. If they are distinct, the relation represents a function. If not, then not.

Equation

Try to express `y` in terms of `x` and see if you get a well-defined unique value for `y` wherever defined. If you do, then you have a function, if not, then not.

For example, `x^2+y^2 = 25`

Then `y = +-sqrt(25-x^2)` is not uniquely defined, so the relation fails the 'vertical line test' and is not a function.