This article is the product of an on-going research project about the influences of the didactic contract in the learning of mathematics, and especially regarding the concept of function. This project emerged from preoccupation with the typical collective failure or low academic performance of students in mathematics class, and from the importance of the concept of function in the compulsory teaching of high school and undergraduate university level. We identified didactic and epistemological learning obstacles with the objective of achieving a clearer evaluation of possible hereditary and non-hereditary intellectual difficulties, based on the study of their genesis and historical evolution, as well as of the conceptions held by teachers who induced the presentation of this concept., this based on the adaptations made by the introduction of didactic objects, which permitted the transposition of this mathematical object of knowledge into a school object of knowledge. Some obstacles were found to be present in the implicit clauses of the didactic contract in the learning of the concept, which manifest themselves in students at the moment of demonstrating what they know about the topic.