The Basics About Functions

This page includes the basics about what a function is and the history of functions.

A History

The history behind functions is surprisingly not a very long one with how much of a focus is on it in beginning math classes. I will start this history by discussing the development of the coordinate plane. Although it is not necessary to graph a function it is something that is heavily focused on. Rene Descartes is credited for the creation of the coordinate plane and often times called the Cartensian Plane in his honor. The development goes way before his time and is often taken back to the Ancient Greeks and the ancient peoples work with latitude and longitude. Have you noticed those lines and the cartesian plane are pretty similiar? So we will be jumping forward quite a bit with Rene Descartes. Rene Descartes was known for having poor health and insisting that he needed to stay in bed until he felt fit to rise. It was rumored that he was watching a fly one morning, crawl on his ceiling and was wondering how we would tell someone were that fly was located as it changed position on the ceiling. For more on the history of the discovery of a coordinate plane system back through the ancient Greeks click here and scroll through the short stories.

Now on to the history of functions! From the 'History of Mathematics, An Introduction' by David M. Burton it says,

'The word function appeared in print for the first time in articles by Leibniz in 1692 and 1694, where it was used to designate a geometric object (tangent, subtangent, or normal)connected with a point on a curve (pg. 611).' It might dismay you to also learn that the mathematician Euler considered something a function only if it could be represented as one expression under its domain. Therefore, piecewise functions were not considered functions to Euler in their early development. He only considered functions that we would now consider nice functions. I know many of you are groaning at the very fact that we do now consider them functions but it was not long before Euler broaden his view of a function as well. The development of the broadest definition of a function was done by Dirichlet and was the accepted definition from about 1837 through the rest of the 19th century:

'y is a function of the variable x, defined on the interval a < x < b, if to every value of the variable x in this interval there corresponds a definite value of the variable y. Also, it is irrelevant in way this correspondence is established (Burton 162).'



Functions have led to so many beautiful things in mathematics such as calculus! I invite you, once you have learned all you can from these pages, to continue to look deeper into the influence functions have had in mathematics.


Informational Video About Functions: Khan Academy-What is a Function?

For a different view of functions check on this geogebra applet!