Graphical Transformations

Tutorial Videos

A-Level Maths: B9-02 [Graph Transformations: Investigating y = f(x) + a]

A-Level Maths: B9-02 [Graph Transformations: Investigating y = f(x) + a] by TLMaths

Transformations of Graphs (translations) : ExamSolutions

Transformations of Graphs (translations) : ExamSolutions by ExamSolutions

The Transformation y=f(x)+a. Example y=f(x)+2 Is A Translation 2 Units Up.

The Transformation y=f(x)+a. Example y=f(x)+2 Is A Translation 2 Units Up. by Maths Mark

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Translating (shifting) functions: Videos & practice

Activities & Resources

• Interactive Maths
  • f(x) + b: Graph Transformations 1
• Mr Draper Maths Transformations of Functions: Translation
  • Reasoning With Functions and Translations of Graphs
• BossMaths
  • A13a Translations & Reflections of Functions✦ (Translations & reflections)

Worksheets

• MME
  • Graph Transformations y-stretch & y-shift (drill): Questions | Answers

Dr Frost Video

Key Skill – Understand the effect of the transformation y = f(x)+a.

K586: Understand the Effect of the Transformation y=f(x)+a.

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 448b: Sketch the graph y = f(x) + a given the graph of y = f(x) (not yet active)
• 448d: Understand the effect on a point under the transformation y = f(x) + a
• 448: Exam Practice: Graph transformations of y = f(x+a) and y = f(x) + a

Tutorial Videos

A-Level Maths: B9-05 [Graph Transformations: Investigating y = kf(x)]

A-Level Maths: B9-05 [Graph Transformations: Investigating y = kf(x)] by TLMaths

Transformations of Graphs (stretches) : ExamSolutions

Transformations of Graphs (stretches) : ExamSolutions by ExamSolutions

Graph Transformations : y=3f(x) and y=f(2x)

Graph Transformations : y=3f(x) and y=f(2x) by Oxford Mathematics Education – Yarm

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Stretching (scaling) functions: Videos & practice

Activities & Resources

• Don Steward
  • Parabola Template and Stretched Graphs
• Interactive Maths
  • cf(x): Graph Transformations 4

Worksheets

Dr Frost Slides & Activities

• Dr Frost Slides (4)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 450a: Sketch a graph of y = af(x) given the graph of y = f(x)
• 450c: Understand the effect on a point under the transformation y = af(x)
• 450: Exam Practice: Graph transformations of y = f(ax) and y = af(x) (dilations)

Tutorial Videos

A-Level Maths: B9-08 [Graph Transformations: Investigating y = -f(x)]

A-Level Maths: B9-08 [Graph Transformations: Investigating y = -f(x)] by TLMaths

Transformations of Graphs : Reflections y = – f(x), f(-x) : ExamSolutions

Transformations of Graphs : Reflections y = – f(x), f(-x) : ExamSolutions by ExamSolutions

Function Transformations: Reflections Across the x-axis and y-axis

Function Transformations: Reflections Across the x-axis and y-axis by Mathispower4u

Online Platforms (with Videos & Exercises)

Activities & Resources

• Mr Draper Maths Transformations of Functions: y=-f(x) and y=f(-x)
  • Transformations of Functions: -f(x) and f(-x)

Worksheets

Dr Frost Video

Key Skill – Understand the effect of the transformations y = -f(x) and y = f(-x).

K587: Understand the Effect of the Transformations y=−f(x) and y=f(−x).

Dr Frost Slides & Activities

• All in one summary sheet

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 449a: Sketch a graph of y = -f(x) given the graph of y = f(x)
• 449c: Understand the effect on a point under the transformation y = -f(x)
• 449: Exam Practice: Graph transformations of y = f(-x) and y = -f(x)

Further Practice

• Practise Questions (may include angles in a triangle and on a straight line)

Tutorial Videos

A-Level Maths: B9-03 [Graph Transformations: Investigating y = f(x – a)]

A-Level Maths: B9-03 [Graph Transformations: Investigating y = f(x – a)] by TLMaths

Graph transformation y = f(x+a) of the function f(x)

Graph transformation y = f(x+a) of the function f(x) by MathsMasterOrg

Transformations of Graphs (translations) : ExamSolutions

Transformations of Graphs (translations) : ExamSolutions by ExamSolutions

Online Platforms (with Videos & Exercises)

Activities

• Interactive Maths
  • f(x + a): Graph Transformations 2
• MEI
  • Translating quadratic graphs✦

Worksheets

• MME
  • Graph Transformations x-stretch & x-shift (drill): Questions | Answers

Dr Frost Video

Key Skill – Understand the effect of the transformation y=f(x+a).

K585: Understand the Effect of the Transformation y=f(x+a).

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 448a: Sketch the graph y = f(x + a) given the graph of y = f(x) (not yet active)
• 448c: Understand the effect on a point under the transformation y = f(x + a)
• 448: Exam Practice: Graph transformations of y = f(x+a) and y = f(x) + a

Further Practice

• Practise Questions

Tutorial Videos

A-Level Maths: B9-06 [Graph Transformations: Investigating y = f(kx)]

A-Level Maths: B9-06 [Graph Transformations: Investigating y = f(kx)] by TLMaths

Graph Transformations : y=3f(x) and y=f(2x)

Graph Transformations : y=3f(x) and y=f(2x) by Oxford Mathematics Education – Yarm

Transformations of Graphs (stretches) : ExamSolutions

Transformations of Graphs (stretches) : ExamSolutions by ExamSolutions

Online Platforms (with Videos & Exercises)

Activities

• Interactive Maths
  • f(dx): Graph Transformations 5

Worksheets

Dr Frost Video

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 450b: Sketch a graph of y = f(ax) given the graph of y = f(x)
• 450d: Understand the effect on a point under the transformation y = f(ax)
• 450: Exam Practice: Graph transformations of y = f(ax) and y = af(x) (dilations)

Further Practice

• Practise Questions

Tutorial Videos

A-Level Maths: B9-09 [Graph Transformations: Investigating y = f(-x)]

A-Level Maths: B9-09 [Graph Transformations: Investigating y = f(-x)] by TLMaths

Graphing Reflections y=-f(x) or y=f(-x)

Graphing Reflections y=-f(x) or y=f(-x) by Carole Del Vecchio

Transformations of Graphs : Reflections y = – f(x), f(-x) : ExamSolutions

Transformations of Graphs : Reflections y = – f(x), f(-x) : ExamSolutions by ExamSolutions

Online Platforms (with Videos & Exercises)

Activities

Worksheets

Dr Frost Video

Key Skill – Understand the effect of the transformations y = -f(x) and y = f(-x).

K587: Understand the Effect of the Transformations y=−f(x) and y=f(−x).

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 449b: Sketch a graph of y = f(-x) given the graph of y = f(x)
• 449d: Understand the effect on a point under the transformation y = f(-x)
• 449: Exam Practice: Graph transformations of y = f(-x) and y = -f(x)

Further Practice

• Practise Questions

Tutorial Videos

Transformations of Graphs – Corbettmaths

Corbett Maths Transformations of Graphs (Reflections & Translations Only)

Transforming Trigonometric Graphs – Corbettmaths

Corbett Maths Transforming Trigonometric Graphs (Reflections & Translations Only)

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Combining function transformations: Videos & practice

Activities

• Maths 4 Everyone
  • Transformations of Functions Loop: Set 1 · Set 2
• Pixi Maths
  • Introduction to Functions ppt (Slides 8-11) can be used before introducing Graphical Transformations
  • Transformations of Graphs ppt
  • Transformations of Graphs Starter
• Andy Lutwyche
  • Transforming Functions Spiders
  • Transforming Functions (Coordinates) Codebreaker
  • Transforming Functions – Fill In The Blanks
  • Coordinates and Transforming Functions Codebreaker
  • Coordinates on Functions Codebreaker
  • Tranforming Functions (Coordinates) Spiders
  • Transforming Functions Worksheet
  • Transforming Trigonometric Functions
• Math = Love (Sarah Carter)
  • Transforming Linear Functions Foldable
  • Function Transformations Foldable
• Taylor HS
  • Move the Monster Worksheet
• Don Steward
  • Graph Transforms✦
  • Translating y = x Squared✦
• Interactive Maths
  • All Transformations Combined: Graph Transformations 6
• Go Teach Maths
  • Transformations of Graphs
  • Transformations of Graphs (IGCSE)
• Desmos
  • Marbleslides: Parabolas (transform parabolas so the marbles pass through the stars)
  • Function Transformations: Practice with Symbols (GCSE) (by Natalie Vernon: describe transformations in words and with f(x) notation)
• Jo Morgan
  • Transforming parabolas✦

Worksheets

• Dr Austin Maths
  • Investigating Graphs (Word | PDF | Answers)
  • Drawing Graphs Practice Grid (Word | PDF✦ | Answers✦)
  • Describing Graphs Practice Grid (Word | PDF✦ | Answers✦)
  • Points on Graphs Practice Grid (Word | PDF✦ | Answers✦)
• Corbettmaths (Reflections & Translations Only)
  • Transformations of Graphs Practice Questions✦ & Solutions
• Pixi Maths
  • Transformations of Graphs RAG
• WW
  • Transformations of Graphs Booklet Word Doc & PDF
  • Grids Word Doc & PDF
• Miss Konstantine (MathsHKO)
  • Graph Transformations MCQ
• MME
  • Graph Transformations (exam style): Questions | Answers  •  Graph Shifts & Stretches Mixed (drill): Questions | Answers
• 1st Class Maths
  • GCSE Style Questions – Graph Transformations✦ (answers✦)
• MadAsMaths (T. Madas)
  • Transformations Of Graphs Practice Q1, 4 · questions only
• Mr Morley Maths
  • Transforming Graphs: Notes jotter/worksheet · Exam questions · Mark scheme

Dr Frost Video

Key Skill – Understand the effect of the transformation y=f(x+a).

K585: Understand the Effect of the Transformation y=f(x+a).

Key Skill – Understand the effect of the transformation y = f(x)+a.

K586: Understand the Effect of the Transformation y=f(x)+a.

Key Skill – Understand the effect of the transformations y = -f(x) and y = f(-x).

K587: Understand the Effect of the Transformations y=−f(x) and y=f(−x).

Key Skill – Determine the equation of a new curve given a transformation drawn on a graph.

K588: Determine the Equation of a New Curve Given a Transformation Drawn on a Graph.

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 448e: Apply transformations y=f(x+a) and y=f(x)+a in a table. (not yet active)
• 448f: Sketch the graphs of trigonometric functions y=sin(x)+a or y=sin(x+a)
• 448g: Determine the equation in f(x) after a translation of a given graph to f(x)+a and f(x+a)
• 448h: Describe the translation of a function given the equations before and after. (not yet active)
• 448i: Determine the new equation of a function after a translation by beginpmatrixa0endpmatrix or beginpmatrix0aendpmatrix
• 449e: Sketch the graphs of trigonometric functions y=-sin(x) or y=sin(-x)
• 449f: Determine the equation in f(x) notation after a reflection of a given graph in one axis only.
• 449g: Determine the new equation of a function after a reflection in one axis only.
• 449h: Describe a reflection given the equations of the original and transformed functions. (not yet active)
• 450e: Apply transformations y=f(ax) and y=af(x) in a table. (not yet active)
• 450f: Sketch the graphs of trigonometric functions y = asin(x) or y = sin(ax)
• 450g: Determine the new equation in f(x) notation after the transformation of a given graph to y=af(x) or y=f(ax)
• 450h: Determine the new equation of a function after a scaling transformation y=f(ax) or y=af(x) (not yet active)
• 448: Exam Practice: Graph transformations of y = f(x+a) and y = f(x) + a
• 449: Exam Practice: Graph transformations of y = f(-x) and y = -f(x)
• 450: Exam Practice: Graph transformations of y = f(ax) and y = af(x) (dilations)

Further Practice

• Practise Questions

Tutorial Videos

Graph Transformations | Grade 7-9 Maths Series | GCSE Maths Tutor

Graph Transformations | Grade 7-9 Maths Series | GCSE Maths Tutor by The GCSE Maths Tutor

A-Level Maths: B9-22 Graph Transformations: Examples of Describing Two Transformations

A-Level Maths: B9-22 Graph Transformations: Examples of Describing Two Transformations by TLMaths

Transformation of Graphs: y=f(x) into y=2f(x+1) – Quick Explanation

Transformation of Graphs: y=f(x) into y=2f(x+1) – Quick Explanation by AcademicLeadersEducation

Transformations of Trig. Graphs y=f(x)+a type: ExamSolutions

Transformations of Trig. Graphs y=f(x)+a type: ExamSolutions by ExamSolutions

Online Platforms (with Videos & Exercises)

Activities

• Interactive Maths
  • f(x + a) + b: Graph Transformations 3
• Jamie Wood (@jamiewoodmaths)
  • Order of transformations: interactive tool✦

Worksheets

• MadAsMaths (T. Madas)
  • Transformations Of Graphs Practice Q2–3, 5 · questions only

Dr Frost Video

Dr Frost Slides & Activities

• Slides & Worksheet

Topic Test

• Standard Test

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 451a: Sketch the graph y = f(x + a) + b given the graph of y = f(x)
• 451b: Sketch the graph y = af(bx) given the graph of y = f(x) (not yet active)
• 451c: Sketch the graph af(x)+b, af(x+b) and f(ax)+b given the graph of y = f(x)
• 451d: Sketch the graph of a trigonometric function given in the form y = sin(x + a) + b
• 451e: Sketch the graph of a trigonometric function given in the form y = asin(bx) (not yet active)
• 451f: Sketch the graph of a trigonometric function given in the form y = asin(x+b), y = asin(x)+b or y = sin(ax)+b (not yet active)
• 451g: Determine the constants of a trigonometric function given in the form y = asin(x+b), y =asin(bx)+c or y = asin(x+b) + c given its sketch.
• 451h: Determine the equation in f(x) notation after a translation of a given graph to y = f(x + a) + b (not yet active)
• 451i: Determine the equation in f(x) notation after the transformation of a given graph to y = af(bx) (not yet active)
• 451j: Determine the equation in f(x) notation after the transformation of a given graph to y = af(x)+b, y = af(x+b) or y = f(ax)+b (not yet active)
• 451k: Describe the translation of a function y=x² to y=(x+a)²+b (not yet active)
• 451l: Determine the new equation of a function after a translation by a given vector beginpmatrixabendpmatrix (not yet active)
• 451m: Determine the new equation of a function after transformations given in the form y = af(bx) (not yet active)
• 451n: Determine the new equation of a function after a combination of transformations, y = af(x)+b, y = af(x+b) and y = f(ax)+b (not yet active)
• 416a: Determine the minimum point of a quadratic graph when given in completed square form.
• 416c: Determine the maximum point of a quadratic graph when given in completed square form.
• 416b: Determine the original quadratic function given the maximum or minimum point.
• 451: Exam Practice: Combinations of graph transformations

Further Practice

• Practise Questions