Definition:Function/Historical Note

Historical Note on Function
The term function, as used in the modern sense, was first used by in $1694$.

The notation $f \left({x}\right)$ itself appears to have originated with.

Up until the time of, it was accepted that a function was limited to various classes of expression: a polynomial, a finite combination of elementary functions, a power series or a trigonometric series.

made the claim that a function of arbitrary shape could be represented by a trigonometric series.

It was not until in $1837$ that the modern definition of function was formulated.