What was the notation for functions before Euler? According to the Wikipedia article, 

[Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.
  — Leonhard Euler, Wikipedia

What was the notation for functions before him?

Let's observe an example :
$a)$ formal description of function (two-part notation)
$f : \mathbf{N} \rightarrow \mathbf{R}$
$n \mapsto \sqrt{n}$
$b)$ Euler's notation :
$f(n)=\sqrt{n}$
I don't know who introduced two-part notation but I think that this notation must be older than Euler's notation since it gives more information about function and therefore two-part-notation is closer to correct definition of the function than Euler's notation.
There is also good wikipedia article about notation for differentiation.
