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GCSE Graph Transformations Revision Guide
Foundation
Higher Tier
Exam Practice
Formulae
Mastering Function Changes
Graph transformations allow us to take a known function, like y = x², and modify its position or shape on the coordinate plane. By applying simple mathematical rules to either the input (x) or the output (f(x)), we can shift, reflect, or stretch the curve. This is a vital skill for GCSE Higher Tier students, often appearing in the final sections of non-calculator papers.
Key Tip: Transformations inside the bracket affect the x-axis (horizontally).
Quick Navigation
Reflections
Stretches
Translations
Combined Transformations
Essential Formulae
y = f(x) + a
Shifts the entire graph vertically upward by a units. The x-coordinates remain unchanged.
Vertical Translation
Horizontal Translation
y = f(x − a)
Shifts the entire graph horizontally to the right by a units. The y-coordinates remain unchanged.
Vertical Stretch
y = af(x)
Stretches the graph vertically by a scale factor of a. All y-coordinates are multiplied by a, while the x-coordinates remain unchanged.
Lesson Modules
Translations
Learn how to move graphs left, right, up, and down using vector notation.
Combined
Combine multiple transformations in the correct order for high-mark questions.
Reflections
Understand how to flip graphs over the x-axis and y-axis using negative coefficients.
Stretches
Explore horizontal and vertical scale factors and how they impact the slope.
Core Subtopics
Structured lessons for every syllabus requirement.
Worked Example
Worked Example: Reflecting f(x) in the x-axis
THE QUESTION
"The curve C has the equation y = f(x). The point P(3, 5) lies on curve C. Find the coordinates of point P after the transformation y = -f(x)."
Method
- Identify that y = -f(x) is an outside transformation.
- Outside transformations affect the y-values only.
- A negative sign outside means reflection in the x-axis.
- Multiply the original y-coordinate by -1.
Common Mistake
Students often forget to factorise the coefficients or miss the common variable. Resulting in incomplete answers like 6(x² + 2x) or x(6x + 12).
Final Answer
(3, -5)
Revision Resources
Worksheet
15 Questions (PDF)
Interactive Quiz
Timed Practice
Exam Questions
Past Paper Hub
Mark Scheme
Step-by-Step Guide
Playlist
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Expert Video Tutorials
Related Topics
Frequently Asked Questions
Why does y = f(x - a) move the graph to the right and not the left?
It’s about what value of x is needed to get the same output as the original. If we subtract ‘a’ from x before the function sees it, we need x to be ‘a’ units larger to produce the same result, thus shifting the whole shape in the positive direction.
What is the ctransformationsorrect order for combined ?
It’s about what value of x is needed to get the same output as the original. If we subtract ‘a’ from x before the function sees it, we need x to be ‘a’ units larger to produce the same result, thus shifting the whole shape in the positive direction.
Does this topic appear on Foundation tier papers?
While basic translations and reflections can appear on Foundation, complex combined transformations and horizontal stretches are exclusive to the Higher Tier curriculum.
