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

1 Answer
Nov 3, 2015

Answer:

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.