When can we say that a relation is not a function?

Answer 1

When it doesn't fulfill the requirements of a function. A function must have EXACTLY ONE value of one of the variables (the "dependent variable") for every value of the other variable or variables (the "independent variable").

Answer 2

The relation is a function if, for every element in the domain there is exactly one element in the range and if for every element in the range there is at least one element in the domain.