TITLE: What was the notation for functions before Euler?
QUESTION [12 upvotes]: 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?

REPLY [2 votes]: The question is ill-posed, as there was no concept of function before Bernoulli and Euler in anything approaching the modern sense. 
Leibniz and Bernoulli mostly worked with variable quantities.  Thus, a curve may be defined by an equation involving both $x$ and $y$ and the functional relation between $x$ and $y$ was only implicit, because neither was chosen as the independent variable upon which the other would depend.  Similarly, what we would today call differentiation involved relations among infinitesimal differentials $dx$ and  $dy$.  What we would today express as the idea of independent variable was expressed by saying that $dx$ varies in constant increments.
Since there was no concept there could not have been a notation for it. Thus, in the 17th century mathematicians mainly worked with curves defined by an equation, and studied there properties. This does not require anything close to the modern notion of a function and they did not have one, though Leibniz did realize the functional relationship between $x$ and $y$ along a curve.