DBMS – Normalization
Function and relation
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! But 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.