This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper excerpts from the lectures of three teachers at one university are analysed, using commognitive theory. Characteristic features of the teachers’ discourses about functions are presented. Definitions are found to be the central type of narrative, while theorems and proofs are largely absent, despite the fact that the teaching is of a traditional type, often connected to the “definition-theorem-proof” format. Three main categories of routines are found: substantiation, construction and motivation routines. It is also seen that the teachers are more concerned with questions of “why” to do things than “when” to do them.