Fiducia TogetherFunctions and graph transformations
A rule taking an input to an output, and what happens when you shift or stretch it.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A function maps each input to exactly one output, written f(x). Composite functions apply one after another; inverse functions reverse the mapping.
Where it applies
Higher tier maths.
How it works
Graph transformations follow rules: f(x) + a shifts up, f(x + a) shifts left, −f(x) reflects in the x-axis, f(−x) reflects in the y-axis.
The counter-intuitive one is that changes inside the bracket move the graph in the opposite direction to the sign.
How to use it in your work
For composite functions, work from the inside out and write each stage.
For transformations, state the transformation in words as well as showing it. Questions ask you to describe.
To find an inverse, swap x and y then rearrange.
Where to get help
Your teacher and your board's specification and mark scheme.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.