This IB Maths AA HL Topic AHL 2.13 – Advanced Rational Functions resource develops students’ understanding of rational functions with linear and quadratic expressions in the numerator and denominator. It begins by reviewing the key features required in a complete graph, including intercepts, domain restrictions, and horizontal, vertical, and oblique asymptotes. Students learn how the relative degrees of the numerator and denominator determine end behaviour and how polynomial division can be used to identify oblique asymptotes.

The lesson also develops confidence in analysing and sketching rational functions systematically. Students practise finding domains, asymptotes, x- and y-intercepts, and the key features needed to produce accurate graphs. Particular attention is given to distinguishing genuine vertical asymptotes from removable discontinuities or holes caused by cancelled factors. The resource also extends students’ understanding through rational inequalities and a technology-based investigation using Desmos, GeoGebra, or a GDC. With clear explanations, worked examples, graphing practice, exam guidance, investigation tasks, and fully worked solutions, this resource helps HL students build strong graphical and algebraic fluency in line with IB Mathematics AA expectations.