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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Graph Transformations Questions and Answers

Graph Transformations questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.

Practise graph transformations in Unit 4 →Graphs, Sequences and Calculus revision notes

What this topic covers

Graph Transformations worked examples

Worked example 1: Translations of graphs

The point \((1,\ 4)\) lies on \(y=\mathrm{f}(x)\). Find the image on (a) \(y=\mathrm{f}(x)+2\) (b) \(y=\mathrm{f}(x+3)\).

Solution

  1. (a) Up 2: \((1,\ 6)\).
  2. (b) Left 3: \((-2,\ 4)\).

Answer: (a) \((1,6)\) (b) \((-2,4)\)

Tip: Changes inside the bracket act on x in the opposite direction.

Worked example 2: Stretches of graphs

The point \((6,\ -1)\) lies on \(y=\mathrm{f}(x)\). Find the image on (a) \(y=2\mathrm{f}(x)\) (b) \(y=\mathrm{f}(3x)\).

Solution

  1. (a) Vertical stretch factor 2: \((6,\ -2)\).
  2. (b) Horizontal stretch factor \(\tfrac{1}{3}\): \((2,\ -1)\).

Answer: (a) \((6,-2)\) (b) \((2,-1)\)

Tip: f(3x) squashes towards the y-axis.

Worked example 3: Combined transformations

The point \((2,\ 3)\) lies on \(y=\mathrm{f}(x)\). Find its image on \(y=-\mathrm{f}(x)+1\).

Solution

  1. Reflect in the x-axis: \((2,\ -3)\).
  2. Then translate up 1: \((2,\ -2)\).

Answer: \((2,\ -2)\)

Tip: Apply the reflection before the translation here.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise graph transformations for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test graph transformations?

Either Higher tier paper, 1H or 2H, can test graph transformations: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more graph transformations questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions