[Bob]

The definition in my book says domain is all the x alues and range is all the y values.

That is the most braindead definition I’ve ever heard. Did anybody really print a book containing such nonsense?

I think that the kid was misstating what he read. The domain does consist of x values and the range does consist of y values, just not necessarily all of them.

[cartan]

I was unhappy about the term “x values.” What are the “x values” of the function

f : ℜ → ℜ
t ↦ t2

It’s not like variables being called x or y was an essential part of the definition of a function.