IB Maths AA SL 2.8 - Reciprocal and Rational Functions

This IB Maths AA SL Topic 2.8 – Reciprocal and Rational Functions resource introduces students to the key features of reciprocal and rational functions and develops confidence in interpreting, sketching, and analysing their graphs. It begins with the reciprocal function, covering its domain, range, asymptotes, intercepts, and self-inverse nature, before extending this understanding to rational functions of the form (ax+b)/(cx+d). Students are guided through identifying horizontal and vertical asymptotes, finding intercepts, and understanding how algebraic structure determines the shape and position of the graph.

The lesson also develops fluency in moving between equations and graphical features, including finding the equation of a rational function from given asymptotes and intercepts. With clear explanations, worked examples, graph-sketching practice, structured problem-solving, and fully worked solutions, this resource helps SL students build a strong understanding of reciprocal and rational functions in line with IB Mathematics AA expectations.