GCSE Higher Composite and Inverse Functions + Transformations Lesson

A complete GCSE lesson introducing composite functions, inverse functions and function transformations with real life examples and clear visual flow charts.

• Ideal for GCSE crossover to higher tier
• Introduces functions, notation and flow charts
• Real life applications including currency conversion
• Step by step examples of composite and inverse functions
• Clear visuals showing transformations of graphs
• Opportunities for reasoning and structured practice
• Fully editable and suitable for mixed ability classes

This lesson introduces composite and inverse functions through accessible real life examples. It begins with a currency conversion activity that helps learners recognise how linked steps create a chain of operations. Flow charts are used throughout to show the order of calculations clearly and build confidence with function notation.

Learners explore composite functions such as f(g(x)) with worked examples, then move on to transformations including vertical and horizontal shifts, stretches and compressions. Visuals and graphs help students understand how these changes affect the shape and position of functions.

Inverse functions are introduced through simple step by step examples, showing how to reverse operations and verify that f and f⁻¹ work together correctly. The lesson ends with a short practice task and reflection questions that strengthen understanding.

This resource works well for GCSE crossover to higher tier learners and is fully editable for classroom use.