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
