Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz was the first mathematician to use the term function. 

If every value of x is associated with exactly one value of y, then y is a function of x. This is expressed by y = f(x). An example of a one-to-one function, which has the inverse constraint that every y must be associated with exactly one value of x, is y = x² if x and y are both positive. If negative values of x are also allowed, it becomes a one-to-many function.

Functions involving sines, secants, and the like, are called trigonometric functions. Functions with x as an exponent, like 3^x, are called exponential functions.

Leibniz also invented the calculus independently of Sir Isaac Newton.