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

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

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

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

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

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

Edexcel IGCSE 4MA1 Graph Transformations: Exam Questions

Edexcel IGCSE 4MA1 Graph Transformations: Exam 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.

3 worked examples

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Start with one question on graph transformations. Stuck? Take a hint. No sign-in needed.

Transforming graphs. A curve

y = f (x)

passes through

(1, - 5)

. After the curve is transformed to

y = f (2 x)

, where has that point moved to?

Choose your answer · keys 1–4

(\frac{1}{2}, - 5)

(1, - 10)

(2, - 5)

(1, - 5)

What this topic covers

Graph Transformations 1: f(x)+a, f(x+a): Vertical/horizontal shifts of y = f(x).
Graph Transformations 2: af(x), f(ax): Vertical/horizontal stretches of y = f(x).
Graph Transformations 3: Combined: Combining two or more graph transformations.

Graph Transformations worked examples

Worked example 1: Translations of graphs

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

Solution

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

3 steps

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

Worked example 2: Stretches of graphs

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

Solution

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

3 steps

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

Worked example 3: Combined transformations

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

Solution

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

3 steps

Tip: Apply the reflection before the translation here.

Where students lose marks on graph transformations

Examiner's noteGraph transformations of f(x)

Where marks are lost: Reported as a weakness in every series: points are moved the wrong way, or coordinates are read by counting squares rather than using the scale.

Examiners flagged this in 4 exam series (November 2023, June 2024, November 2024, June 2025). Summarised in our own words from Pearson Edexcel examiner reports. Read the full note →

Play with it Translate a parabola: drag the sliders

The dashed curve is y = f(x), where f(x) = x². Change h and k so that y = f(x − h) + k passes through all the points. Write the translation as a vector.

Want more? Open the full Grapher.

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.

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.

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Edexcel IGCSE 4MA1 Graph Transformations: Exam Questions and Answers

Try it first

What this topic covers

Graph Transformations worked examples

Worked example 1: Translations of graphs

Solution

Worked example 2: Stretches of graphs

Solution

Worked example 3: Combined transformations

Solution

Where students lose marks on graph transformations

Revise graph transformations for the exam

Questions students ask

Practise graph transformations with your progress saved

More Unit 4 topics: Graphs & Functions