Geometrical functions: tools in GeoGebra

The notion of a function is central to modern mathematics and the usual modern definition involves a rule which takes each element of the domain X and assigns a unique element in the range Y. Examples, where X and Y are both the set of real numbers, are f(x)=x3, or f(x)=ex. In this article, I’d like to give some examples of geometrical functions as illustrated by the software GeoGebra. GeoGebra is dynamic mathematics software. In this the user can define mathematical objects such as numbers, points, lines, and circles. Most of these objects have two representations, and this dual nature is the essence of GeoGebra.