Relative reference system

This activity belongs to the GeoGebra book Attractive projects. If we redefine a function f (x) as O + t i + f (t) j, where {O, i, j} constitutes the referential system, it is enough to permutate the vectors i and j to obtain the graph of the inverse function (whose domain may need to be restricted, depending on the case, to effectively be a function).
It is also much easier to manipulate geometric objects such as ellipse if we define them vectorially on a relative referential system. In fact, this is what the GeoGebra program does (see the previous PDF on Automatic Animations).
Author of the construction of GeoGebra: Rafael Losada