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Graph transformations describe how y = f(x) changes under translations, stretches and reflections — f(x)+a, f(x+a), af(x) and f(ax). This topic teaches sketching transformed curves and describing combined transformations. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Changes outside the function move it vertically and behave as you expect; changes inside move it horizontally and do the opposite. So f of x plus 2 shifts up, but f of x plus 2 inside shifts left. Stretches follow the same rule, with the inside factor reciprocated.
Before you start
Get graph sketching and function notation straight before you begin. It is Pure 1 content. This is the foundation for trigonometric and exponential graphs. The topic sits within Algebra.
What you learn
The course works through translations, stretches, reflections, combined transformations and find the curve, then transform. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Transformations of Graphs belongs to Algebra and is met in the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Related topics students usually take next include Algebraic Division, Algebraic Fractions and Completing the Square. Endless extra practice on this strand is available on the Algebra revision engine, which generates a fresh question each time.
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