Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features of graphs with little understanding of the actual mathematics concepts involved. We recommended then that visual strategies must be used to improve learner conceptual understanding. This study extends that exploration to investigate the role of visualisation in the learners' conceptual understanding of graphical relationships from the perspective of Peircean semiotics. Semiotics is a key element of mathematical understanding and construction of meaning. The role of semiotics incorporates Vygotsky's semiotic mediation as this influences learners' understanding of graphs and serves as a useful foundation to make sense of learners' responses. This qualitative study is embedded in the interpretivist paradigm and meaning is extracted from a deep analysis of the empirical data in order to explain learners' understanding of graphical functional relationships.