Functions and Graphs Maths Lessons & Worksheets (GCSE, IGCSE & A-Level)

Curriculum Hub → Maths Lessons → Algebra → Functions and Graphs

This page brings together ready-to-teach functions and graphs maths lessons for GCSE / IGCSE and A-Level. Browse the full collection, including function notation, composite and inverse functions, graph translations and stretches, trigonometric transformations, modulus functions, piecewise graphs and combining transformations—with each lesson designed to support clear modelling, independent practice and exam preparation.

  • Ready-to-teach function notation and graph transformation lessons
  • Presentations, worksheets and structured practice
  • GCSE / IGCSE and A-Level coverage
  • Scheme of work links for curriculum planning

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Use the sections below to jump straight to GCSE / IGCSE or A-Level functions and graphs lessons.
Each resource is designed to reduce planning time and support student progression from fluent notation to confident graph transformation.

Jump to:  GCSE / IGCSE Functions and Graphs  |  A-Level Functions and Graphs

Functions and Graphs: GCSE / IGCSE

These GCSE / IGCSE Higher lessons develop secure function notation before moving into translations, stretches and composite structures. Students learn to interpret f(x), find inputs and outputs, and describe graph transformations using the correct notation. Topics include:

  • Working with functions — calculating inputs and outputs using correct notation
  • Composite functions — interpreting and evaluating fg(x) and related forms
  • Inverse functions — finding inverses using function machines and notation
  • Translating functions — graphs in the form f(x + a) and f(x) + a
  • Stretching functions — graphs in the form af(x) and f(ax)
  • Transforming trigonometric graphs — sin, cos and tan using function notation
  • Solving equations through iteration — approximate solutions using numerical methods

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Algebra: Interactive Lessons
Composite Functions
Ages 14 - 16

Composite Functions

How to find the output of composite functions using the correct notation.
Algebra: Interactive Lessons
Inverse Functions
Ages 14 - 16

Inverse Functions

How to find the inverse of a function using function machines.
Algebra: Interactive Lessons
Solving Equations Through Iteration
Ages 14 - 16

Solving Equations Through Iteration

How to use numerical methods to solve equations through iteration.
Algebra: Interactive Lessons
Stretching Functions
Ages 14 - 16

Stretching Functions

How to stretch a graph in the form f(ax) and a(fx).
Algebra: Interactive Lessons
Transforming Trigonometric Graphs
Ages 14 - 16

Transforming Trigonometric Graphs

How to transform a sin, cos and tan graph using function notation.
Algebra: Interactive Lessons
Translating Functions
Ages 14 - 16

Translating Functions

How to translate graphs in the form f(x+a) and f(x)+a.
Algebra: Interactive Lessons
Working with Functions
Ages 14 - 16

Working with Functions

How to use the correct notation to calculate outputs and inputs for complex functions.

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Functions and Graphs: A-Level

These A-Level Pure lessons extend function notation into mappings, modulus forms, composite and inverse structures, and combined transformations on non-linear graphs. Students sketch, interpret and solve problems where several transformations or function types appear together. Topics include:

  • Functions and mappings — categorising types of function
  • Composite functions — combining functions to form fg(x)
  • Inverse functions — finding inverses and identifying their properties
  • Translating non-linear functions — translations in the form y = f(x)
  • Stretching non-linear functions — stretches using function notation
  • Combining transformations — multiple transformations on one graph
  • The modulus function — understanding and using |f(x)|
  • Sketching magnitude functions — f(|x|) and |f(x)|
  • Solving modulus problems — equations and inequalities involving modulus
  • Piecewise functions — sketching piecewise graphs and identifying range

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Preview the collection below. Membership unlocks the downloadable PowerPoint presentations, worksheets and full lesson resources for every product.

Algebra: Interactive Lessons
Combining Transformations
Ages 16 +

Combining Transformations

Students learn how to combine graphical transformation using function notation.
Algebra: Interactive Lessons
Composite Functions
Ages 16 +

Composite Functions

Students learn how to combine functions to make a composite function.
Algebra: Interactive Lessons
Piecewise Functions
Ages 16 +

Functions and Mappings

A-Level Mathematics: How to categorise the different types of function.
Algebra: Interactive Lessons
Inverse Functions
Ages 16 +

Inverse Functions

Students learn how to find and identify the properties of an inverse function.
Algebra: Interactive Lessons
Piecewise Functions
Ages 16 +

Piecewise Functions

A-Level Mathematics: How to sketch a piecewise function and identify its range.
Algebra: Interactive Lessons
Sketching Magnitude Functions
Ages 16 +

Sketching Magnitude Functions

Students learn how to sketch magnitude functions in the form f(|x|) and |f(x)|.
Algebra: Interactive Lessons
Solving Modulus Problems
Ages 16 +

Solving Modulus Problems

Students learn how to solve a range of problems involving modulus functions.
Algebra: Interactive Lessons
Stretching Non-Linear Functions
Ages 16 +

Stretching Non-Linear Functions

Students learn how to use function notation to stretch a non-linear functions in the form y = f(x).
Algebra: Interactive Lessons
The Modulus Function
Ages 16 +

The Modulus Function

Students learn how to understand and use the modulus function.
Algebra: Interactive Lessons
Translating Non-Linear Functions
Ages 16 +

Translating Non-Linear Functions

Students learn how to translate a non-linear functions in the form y = f(x).

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