There is only one main thing you need to check in order to see if a mapping between two sets of numbers is a function. You check to make sure each input has a unique output. If your map has two different possible outputs for a given input then it is not a function. It's that simple!
The relation you described is below:
Now, we just look at our inputs:
2, -2, 3, -3
We look to see whether there are two of the same input giving a different output, which we don't!
Therefore, the relation is a function.
Don't get mixed up, though, with this relation! notice that (-2,3) and (3,3) both map their inputs to the same output! However, this is allowed for functions. The main thing for functions is only one possible output for an input, but it doesn't matter if you have many inputs leading to the same output.
I hope that helps you out!