This IB Maths AA HL Topic AHL 2.14 – Odd and Even Functions resource develops students’ understanding of function symmetry, inverse functions, and self-inverse functions. It begins by introducing the algebraic definitions of odd and even functions and connecting these to graphical symmetry. Students learn that odd functions have rotational symmetry of 180° about the origin, while even functions have symmetry about the y-axis, and they practise determining whether functions are odd, even, or neither.

The lesson also explores periodic odd and even functions, including how combined trigonometric functions can affect the overall period of a graph. Students then develop confidence in finding inverse functions algebraically and interpreting them graphically as reflections in the line (y=x). Particular attention is given to the importance of domain restrictions and how these affect the form and domain of an inverse. The resource concludes with self-inverse functions, including algebraic verification, graphical interpretation, domain analysis, and finding intersections with (y=x). With clear explanations, worked examples, graphing tasks, exam tips, and fully worked solutions, this resource helps HL students build a strong understanding of function symmetry and inverses in line with IB Mathematics AA expectations.