Why implicit function is a function?
Well, if it wasn't a function, it couldn't be called an
implicit function ...
Can you say more about what you are thinking, maybe with an example?
The basic idea is that any equation with two variables defines a "relation"; that it, it determines what pairs (x,y) are "related" by satisfying the equation. In some cases, there is only one value of y that pairs up with any given value of x, and then the equation determines y as a function of x. For example, x + y = 5 determines a function, because for any value of x, you can solve for one value of y; but |x| + |y| = 5 does not determine a function, because, for example, if x = 3, y can be either 2 or -2. The former is an implicit function, because it doesn't explicitly tell you what y is; you have to figure that out. And some implicit functions can't actually be solved, so you can't write them explicitly at all, even though they are functions.
Beyond that, we'll need to see what examples you have, and why you think it might not be a function. It will also help if you tell us the definition you were given for "function", since some starting points make this easier to understand than others.