Every function is a relation, but not every relation is a function.
A function is a well-defined relation.
By well-defined we mean the elements are mapped to a unique and a specific image correspondingly. So, the mathematician will be able to study and use all the tools possible to understand and visualize the map.
An example of a relation that is not a function is the Circle. They usually use a vertical line to test if the graph or relation has more than one image at a specific point.
At x=2, we have two images which contradicts the original concept of a function.
