This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies and approaches on these tasks. A cross-sectional study was then made to investigate for a typical trajectory of the growth points. The tasks were fielded to 444 Year 8, 9, and 10 students, first at the start of the school year and then 5 months later. The framework of growth points, and their resonance with similar research elsewhere, offer a research-based framework that can serve as an analytic tool for describing understanding, assessing learning and for pedagogy.