Why does the domain differ for different functions?

At first glance, a function looks just like a relation. Like a relation, a function has a domain and range made up of the x and y values of ordered pairs. It has to do with the first three ordered pairs in the relation ... In this relation, when there is no sale, each input has one and only one output. When this is the case, we call the relation a function. In mathematics, a function is a relation in which no input relates to more than one output. For this type of function, the domain is all real numbers. A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign. There are different ways of looking at functions. We will consider a few. But first, we need to discuss some terminology. A function is a "well-behaved" relation. Just as with members of your own family, some. This is a function. You can tell by tracing from each x to each y. There is only one y for each x; there is only one arrow coming from each x. Ha! Bet I fooled some of you on this one! This is a function! There is only one arrow coming from each x; there is only one y for each x. It just so happens that it's always the same y for each x, but it is only that one y. So this is a function; it's just an extremely boring function! This one is not a function: there are two arrows coming from the number 1; the number 1 is associated with two different range elements. So this is a relation, but it is not a function. Okay, this one's a trick question. Each element of the domain that has a pair in the range is nicely well-behaved. But what about that 16? It is in the domain, but it has no range element that corresponds to it! This won't work! So then this is not a function. Heck, it ain't even a relation!