Summary: The fundamental object of study of mathematics in most of the university career is the concept of a function. For example: the courses have as main objective the study of three operations: limit, derivative and integration on different classes of functions. Nevertheless, the function concept turns out to be one of the most difficult to dominate and to teach, which is due, according to our criterion, to diverse reasons that we expose in our work. One of the objectives of this work is to present a proposal of study of the function concept that facilitates the dominion and motivation by the students. The other objective is to present an application of the procedure for the study of a concept after it has been defined to the study of the function concept.