When is a relation a function? What are some ways to tell if a relation is a function?

The independent variable in a function always generates only one value. For example if the function is y=x², for every x in the domain there is just one value for y. So if x=1 y=1 and if x=-1 y=1. Two different values of x give the same value for y. That’s OK, and this is an example of a function. But x²+y²=1 (unit circle) is not a function because for one value of x, y has two values instead of one.