Why is there so much emphasis on whether osomething is a function

I was tutoring someone for an intro mathematical logic class and there were a few problems about proving something is a function or not. I remember in high school algebra, there were a pretty large emphasis on the vertical line test. In precalculus I saw it again. In calculus I saw it again. In this intro to logic course there was proving that something was a function.



Why does it even matter? After intro to logic I have never really seen a reason why we even care. The only place where it even matters is in complex analysis when you have to define branch cuts for multivalued functions. But it really wasn't that big of a deal, and most people who take high school algebra won't see complex analysis. I could kind of see in a logic class, as an example of proof. But it seems strange that after that class, I have never seen it come up again really. In math or physics or science or anything really.