# Why use notations like $f(x)$ while explaining mathematical proofs or equations etc

If there is a variable "$x$" , and another is "$y$", and let's say I know the relation between them as

$$x= y+1$$

Now, I want to use them in the explanation of some mathematical theory/proof/equation etc. Why a different notation called $f(x)$ ( function of $x$ ) is used to represent $y$ ? Why can't y itself be used ? Cannot i just remember that "$y$" has some relation with "$x$" . Is their some other importance also, other than representing a relation of "$y$" with "$x$", when some term like $f(x)$ is used ?

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Early on, the notion of 'functions' are introduced in much more detail and rigor than the notion of 'dependent variables'. Thus, there is a tendency to phrase things in terms of functions rather than in terms of dependent variables. – Hurkyl Jan 25 '13 at 19:31