A "function" is defined so that an input has a single output. That's the whole idea.
You can repeat outputs of course. So let's say x=5 and x=7 can both output a "3". But no, you can't have an infinite number of outputs from a single input (which is exactly what OP would require).
You can have some kind of thing where you extrapolate a finite number of inputs into an infinite number of inputs, and then map those. So like, take 6 points. Draw lines between them. There you go, now you have an infinite number of outputs from a finite number of inputs. But your method for doing this will determine the whole thing
