if the all the domain (x-value) of the relation (ordered pair) is uniquely matched with the range (y-value) of the the relation, then the relation is function. If the domain (x-value) of an ordered pair is matched with two or more than two range (y-value), then it is not a function.
For example:
A = { (3,2) (4,8) (5,6) (9,0) }
Here, relation A is a function because all the domain (x-value) is uniquely matched with the range (y-value) of the relation A.
B = { (3,2) (4,8) (4,9) (7,0) (8,0) }
Here, Relation B is not a function because the domain {4} is matched with with two ranges {8} and {9}.
C = { (3,2) (4,2) (5,2) (6,0) (7,0) }
Is this a function?? Yes! relation C is a function because all the domain of relation A is uniquely matched with the ranges of relation C. ((You might think that two or more domains are matched with same range. So, it is not a function. But thats not it.)) It doesn't mater whether the range is matched with two or more domain. But, it does matter when two or more domain is matched with with the same range.
I ATTACHED A PICTURE SO YOU COULD UNDERSTAND BETTER.
