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Transforming graphs y=f(x)

Free Printable Transforming graphs y=f(x) PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 8+)

Download free transforming graphs y=f(x) worksheets (PDF), GCSE maths past paper questions and worked solutions for Transforming graphs y=f(x) (8B). This is a Grade 8+ algebra topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from IGCSE MT, Maths Genie, Corbett Maths, Maths Made Easy, Naiker Maths, 1st Class Maths, Metatutor, Maths Takeaway, Dr Austin, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our transforming graphs y=f(x) revision notes and worked examples with diagrams, try real GCSE past paper transforming graphs y=f(x) questions with step-by-step solutions, or download a PDF of all transforming graphs y=f(x) worksheet links.

Free Transforming graphs y=f(x) PDF Worksheets & Answers

Grade 8+ • Topic 8B
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
IGCSE (9–1) past paper booklet
 Qs Ans
Graded exam questions & solutions
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Practice Questions & answers
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MME worksheet & model answers
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Exam question booklet & solutions
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Edexcel exam questions & solutions
 Qs Ans
AQA exam questions & solutions
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Topic worksheet & worked solutions
 Qs Ans
GCSE Maths Takeaway exam questions
 Qs Ans
Practice grid / worksheet & answers
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Practice questions & answers
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Desmos graphing
Interactive online resource
 Open
Self-marking online worksheet
 Page
Grade 8+ topics
8A - Quad. sim. equations8B - Transforming graphs y=f(x)
8C - Algebraic proof8D - Completing the square
8E - Quadratic inequalities8F - Quadratic sequences
8G - Velocity time graphs8H - Circles and tangents
8J - Circle theorem proof8K - Vector proof
8L - Probability equation questions8M - Invariant points
8N - Spheres, cones and cylinders8P - Volume of a frustum
GCSE Maths Grade 8+ Revision Notes & Method

Guide to Transforming graphs y=f(x): Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

Changes outside the bracket affect the y-coordinates as expected, whereas changes inside the bracket affect the x-coordinates in the opposite direction:

• y = f(x) + a translates by vector 0a (up by a);  y = f(x + a) translates by vector −a0 (left by a).
• y = −f(x) reflects in the x-axis (y changes sign);  y = f(−x) reflects in the y-axis (x changes sign).

Example 1: The curve y = f(x) has a turning point at P(3, −4). Find the coordinates of the turning point on: (a) y = f(x − 2) + 5  (b) y = −f(x).

f(x) P(3, −4) −f(x) (3, 4) (5, 1) f(x−2)+5

Solution:

(a) Inside (x − 2) shifts right by 2: x = 3 + 2 = 5
Outside (+ 5) shifts up by 5: y = −4 + 5 = 1 ⇒ (5, 1)
(b) y = −f(x) reflects in the x-axis (multiply y by −1):
Answer: (a) (5, 1)   (b) (3, 4)

Example 2: Given f(x) = x2 − 4x, find the equation of the curve after a reflection in the y-axis followed by a translation of 0−3.

Solution:

Reflection in y-axis replaces x with −x:
f(−x) = (−x)2 − 4(−x) = x2 + 4x
Translation by 0−3 subtracts 3 from the function:
Answer: y = x2 + 4x − 3
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Transforming graphs y=f(x) Questions & Answers

Past Paper Example 1 GCSE Jun 2023 2H Q21 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Here is the graph of y = f(x)
xy–6–4–2246–4–224O
(a) On the grid below, draw the graph of y = f(x) - 4 [1 mark]
xy–6–4–2246–4–224O
(b) On the grid below, draw the graph of y = f(-x) [1 mark]
xy–6–4–2246–4–224O
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
Translation by (0, –4) B1
xy–6–4–2246–4–224O
Answer (a): Trapezium translated 4 units down with vertices (–3, –4), (–2, –3), (–1, –3), (0, –4)
Part (b) Solution:
Reflection in the y-axis B1
xy–6–4–2246–4–224O
Answer (b): Trapezium reflected in the y-axis with vertices (0, 0), (1, 1), (2, 1), (3, 0)
Past Paper Example 2 AQA Jun 2025 1H Q21 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The graph of y = f(x) for 0 ≤ x ≤ 3 is shown.
–4–4–3–3–2–2–1–111223344Oxy
(a) On the grid below, draw the graph of y = -f(x) for 0 ≤ x ≤ 3
The graph of y = f(x) is shown to help you. [1 mark]
–4–4–3–3–2–2–1–111223344Oxy
(b) On the grid below, draw the graph of y = f(x) + 1 for 0 ≤ x ≤ 3
The graph of y = f(x) is shown to help you. [1 mark]
–4–4–3–3–2–2–1–111223344Oxy
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
y = –f(x) reflects the graph in the x-axis B1
–4–4–3–3–2–2–1–111223344Oxy
Answer (a): Triangle with vertices (0, 0), (1, –3), (3, 0)
Part (b) Solution:
y = f(x) + 1 translates the graph 1 unit up B1
–4–4–3–3–2–2–1–111223344Oxy
Answer (b): Triangle with vertices (0, 1), (1, 4), (3, 1)
Past Paper Example 3 IGCSE Jun 2022 1H Q20 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a sketch of part of the curve with equation y = f(x)
yxO(s, t)y = f(x)
There is one maximum point on this curve.
The coordinates of this maximum point are (s, t)
Find, in terms of s and t, the coordinates of the maximum point on the curve with equation
(i) y = f(x - 2) [1 mark]
(ii) y = 3f(x) [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (i) Solution:
Translation 2 units right: (s + 2, t) B1
Answer (i): (s + 2, t)
Part (ii) Solution:
Vertical stretch scale factor 3: (s, 3t) B1
Answer (ii): (s, 3t)

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