IB Maths AA AHL 2.16 - Modulus Functions and Further Transformations

This IB Maths AA HL Topic AHL 2.16 – Modulus Functions and Further Transformations resource develops students’ understanding of advanced transformations involving both the inputs and outputs of functions. It begins with the central distinction between transformations that affect y-values and those that affect x-values, before guiding students through the graphs of (|f(x)|), (f(|x|)), (1/f(x)), (f(ax+b)), and ([f(x)]^2). Students learn how each transformation changes key features of the original graph, including reflections, symmetry, horizontal scaling, translations, asymptotes, zeros, and the sign of the output.

The lesson places particular emphasis on distinguishing (|f(x)|) from (f(|x|)), a common source of errors in examination questions. Students also investigate how zeros of (f(x)) become vertical asymptotes under the reciprocal transformation and how to determine horizontal scale factors and shifts in expressions of the form (f(ax+b)). The resource then develops fluency in solving modulus equations and inequalities using algebraic and graphical methods. With clear explanations, coordinate tables, worked examples, graph-sketching practice, exam warnings, and fully worked solutions, this resource helps HL students build confidence with modulus functions and advanced transformations in line with IB Mathematics AA expectations.