Graph transformation
- Identify whether the change is inside or outside the function.
- Outside changes move vertically.
- Inside changes move horizontally.
Answer: y = f(x) - 2 moves 2 down
𝑥 Algebra
Graph transformations
Learn graph transformations with a GCSE-style explanation, help guide, worked example, practice question and flashcards.
Global XP
Level 10 / 100 XP
1. Explanation
Key idea
- Graph transformations is part of graphs and appears often in KS3–GCSE maths.
- Graph transformations move, stretch or reflect a graph.
- Use the worked model, help guide, interactive question and flashcards to practise graph transformations until the steps feel automatic.
Real-life examples
- Shopping, sport, travel, science, design and everyday decisions all use this skill.
2. Visual
Graph transformations learning map
Understand the key idea → follow the help guide → practise a question → check your method → build speed with flashcards.
3. Help guide
How to tackle Graph transformations
- Learn the rule: Graph transformations move, stretch or reflect a graph.
- Worked model: Identify whether the change is inside or outside the function. Outside changes move vertically. Inside changes move horizontally.
- Try the interactive question without looking at the answer first.
- Use the flashcards to test the rule, the method and a common check.
4. Worked examples
Step-by-step working
5. Interactive questions
Try it yourself
What transformation takes y = x² to y = x² + 3?
6. Flashcards
Master quick recall
Flip each card, then choose whether you know it or need more practice.
0 mastered
FrontRule for Graph transformations
BackGraph transformations move, stretch or reflect a graph.
FrontExample answer: What transformation takes y = x² to y = x² + 3?
Back+3 shifts every y-value up by 3, so it is a translation 3 units up.
FrontCommon check for Graph transformations
BackCheck units/notation, compare with an estimate, and make sure the answer matches the question.
7. Finish
Complete this topic
When you have read the examples, tried the question and reviewed flashcards, claim your topic completion XP.