Graph Transformations Lab

Last updated on Oct 13, 2026

Explore graph transformations with our interactive GCSE Maths Graph Transformations Lab. Discover how translating, reflecting, stretching and compressing functions changes the position and shape of their graphs.

Choose from quadratic, cubic, reciprocal, exponential and absolute value graphs, then use the interactive controls to experiment with different transformations. Watch the graph change instantly, compare it with the original function and see how the equation changes.

Start with simple translations and reflections, or switch to advanced mode to investigate stretches and combinations of transformations. When you're ready, try our 12 graph transformation challenges to test your understanding.

Ideal for GCSE Maths revision, classroom demonstrations and independent learning.

ESHEETS

Graph Transformations Lab

Transformed

y = x 2

y = x² Target

Show parent graph Key features Reference points Explain transformation

Transformation Sequence (from Parent)

y = f(x)

Reflections and stretches are applied to the parent graph first, followed by translations:

No transformation applied — matches the parent graph.

Challenge 1 of 12

Transform y = x² so that it matches the orange dotted target graph.

Horizontal Translation (h)

Shifts left / right inside brackets: f(x − h)

Vertical Translation (k)

Shifts up / down outside function: f(x) + k

Reflections of Parent Graph

Applied to the parent function before translations (h, k)

Vertical Stretch Factor

Stretches parent parallel to y-axis before vertical shift k

Inside Multiplier (b)

f(bx) → Stretches parent parallel to x-axis by factor 1/b