Example9.1.11

Some relations are not functions, because they can't be used to make \(100\%\) accurate predictions. For example, if you have a student's first name and want to determine their student ID number, you probably won't be able to look it up. For a common first name like “Michael,” there will be many student ID number possibilities. Multiple outputs for a single input make “student ID number” not be a function of “first name.”

On the other hand, if we exchange the variables and think of the ID number as the first variable, then there is only one student that ID number applies to, and there is only one official first name for that person. So “first name” is a function of “student ID number.”

in-context