Question

for something to be a function ...

a. only one y value for each x
b. only one x value for each y

Answer 1

Either could be true, but using the convention of y being some function of x, a is true.

Answer 2

ok say for example determine if the relation {3,2) (4,5) (-3,5) (-4,2) is a function

Answer 3

That is a function as far as I can tell. It's possible it isn't though, we can't say for sure without having f(x)= something.