How do I get started on this question?:
Define a function from irrationals to integers by f(a/b) = a - b
(or how the book wrote it) f: Q - Z by f(a/b) = a - b
stop being scared by the math and think about the question as you would any other question of that nature. that's how we start.
lets say i pointed to apple and asked, "is that a dog?" you would respond "no." if i asked "why?" what would you say? well, something along the lines of "well, a dog is a living, breathing thing, it has ears and eyes and fur, etc, since the apple does not have these, it is not a dog."
in other words, to know if something falls under a certain classification, we must know what it means to be in that classification and see if the thing in question fits the bill.
i said all that to say, you need to know what a function is in order to know if something is a function or not. so, what is a function? basically it is a relation where each input value has one and only one output value. is that true in this case? if it is, it's a function, if not, it isn't