The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a concrete problem -- to go beyond the usual one-variable teaching of functions, based on the idea of 'study and research paths' from the anthropological theory of the didactic. In particular, we illustrate the relevance and didactical feasibility of reparametrisation of functions and real work on the fluctuation of variables and parameters in specific intervals.