Is the following relation a function?

x  y
1 −2 
1 −3 
2  1 
3 −2 



No because it has two different y's (outputs), -2 and -3, 
for the same x (input), 1.

A function cannot have two different y's (outputs) for the same x (input).

A function can have two different inputs, x's, giving the same y (output),
but not vice-versa.

The fact that it has two different x's, 1 and 3, giving the same y, -2, 
is not what keeps it from being a function.  What keeps it from being a
function is the two different y's, -2 and -3 for the same x, 1.  

Edwin