Step-by-step Answer:
Whenever two relations that has identical values in the independent variable, i.e. x, or the first variable, but having a different value for the dependent variable, it is NOT a function.
For example, {(5,4),(5,6),(2,3)} is NOT a function because the identical values of the independent variable "5" do not correspond to the same value of the dependent variable.
In other words, when we are given an input of 5, we do not know if the output is 4 or 6, so it is NOT a function.
If the output is defined whenever we are given a valid input, it is a function.
For the given examples,
{(3,5),(-1,7),(3,9)} => NOT a function because when given an input of "3", we cannot determine output.
{(1,2),(3,2),(5,7)} => IS a function, because when we are given any of the valid inputs (1, 3, or 5), we have a unique output.
Similarly the first one,
{(1,2),(1,4),(1,6)} => NOT a function, because we cannot determine a unique output when given an input of "1".