We attend to the composition of even and odd functions, as featured in imagined dialogues between a teacher and students, composed by sixteen teachers in a professional development program. Data were analyzed as aimed at addressing students' intellectual needs, with particular attention to the need for causality and the need for certainty. The results indicate that participants bring into account a myriad of approaches that either complement or replace algebraic definitions of even and odd functions. We provide possible explanations for such a phenomenon in the discussion of the findings.