Transformations

Transformations

Transformations

publish date

May 27, 2025

duration

45:12

Difficulty

Beginner

what you'll learn

Lesson details

Units 1 & 2 (Methods, Transformations)
Focus on understanding algebraic and geometric transformations of functions, including linear, quadratic, and other polynomial forms. Emphasis is placed on domain/range, graphical representations, and algebraic rules governing transformations. These units also cover foundational skills for analyzing functions and modelling real-world scenarios.

Unit 1: Algebraic and Graphical Foundations

1.1 Introduction to Functions and Notation

  • Definition of a function

  • Function notation and evaluation

  • Domain and range (set notation and inequalities)

1.2 Linear and Quadratic Functions

  • Forms of linear functions: gradient-intercept, point-slope

  • Quadratics in standard, factored, and vertex form

  • Techniques for graphing from algebraic form

  • Axis of symmetry, vertex, and intercepts

1.3 Transformations of the Plane

  • Translations: horizontal and vertical shifts

  • Reflections: across the x-axis and y-axis

  • Dilations: vertical and horizontal stretches/compressions

  • Combined (composite) transformations

  • Impact on graphs and equations

  • Identifying transformations from graphs and equations

1.4 Modelling with Functions

  • Using linear and quadratic models in applied contexts

  • Interpretation of parameters (slope, intercept, vertex)

  • Fitting models to data (by hand and with technology)

Unit 2: Further Transformations and Graphical Reasoning

2.1 General Function Transformations

  • Algebraic rules for y = af(b(x + c)) + d

  • Interpretation of parameters a, b, c, and d

  • Application to polynomial and other non-linear functions

  • Transformation of piecewise and absolute value functions

2.2 Inverse and Composite Functions

  • Definition of inverse functions and notation f⁻¹(x)

  • Finding inverses graphically and algebraically (when they exist)

  • Domain and range considerations

  • Composite functions (f ∘ g)(x), evaluation and domain constraints

2.3 Graph Sketching and Analysis

  • Determining function behavior under transformations

  • Symmetry, intercepts, and turning points

  • Sketching without technology

  • Use of CAS/graphing calculators for verification and modelling

2.4 Real-World Modelling and Problem Solving

  • Applying transformations to contextual problems

  • Rewriting equations to interpret features (e.g. maximum profit, minimum cost)

  • Exploring multiple transformations in modelling scenarios

  • Introduction to piecewise models for hybrid systems

Units 1 & 2 (Methods, Transformations)
Focus on understanding algebraic and geometric transformations of functions, including linear, quadratic, and other polynomial forms. Emphasis is placed on domain/range, graphical representations, and algebraic rules governing transformations. These units also cover foundational skills for analyzing functions and modelling real-world scenarios.

Unit 1: Algebraic and Graphical Foundations

1.1 Introduction to Functions and Notation

  • Definition of a function

  • Function notation and evaluation

  • Domain and range (set notation and inequalities)

1.2 Linear and Quadratic Functions

  • Forms of linear functions: gradient-intercept, point-slope

  • Quadratics in standard, factored, and vertex form

  • Techniques for graphing from algebraic form

  • Axis of symmetry, vertex, and intercepts

1.3 Transformations of the Plane

  • Translations: horizontal and vertical shifts

  • Reflections: across the x-axis and y-axis

  • Dilations: vertical and horizontal stretches/compressions

  • Combined (composite) transformations

  • Impact on graphs and equations

  • Identifying transformations from graphs and equations

1.4 Modelling with Functions

  • Using linear and quadratic models in applied contexts

  • Interpretation of parameters (slope, intercept, vertex)

  • Fitting models to data (by hand and with technology)

Unit 2: Further Transformations and Graphical Reasoning

2.1 General Function Transformations

  • Algebraic rules for y = af(b(x + c)) + d

  • Interpretation of parameters a, b, c, and d

  • Application to polynomial and other non-linear functions

  • Transformation of piecewise and absolute value functions

2.2 Inverse and Composite Functions

  • Definition of inverse functions and notation f⁻¹(x)

  • Finding inverses graphically and algebraically (when they exist)

  • Domain and range considerations

  • Composite functions (f ∘ g)(x), evaluation and domain constraints

2.3 Graph Sketching and Analysis

  • Determining function behavior under transformations

  • Symmetry, intercepts, and turning points

  • Sketching without technology

  • Use of CAS/graphing calculators for verification and modelling

2.4 Real-World Modelling and Problem Solving

  • Applying transformations to contextual problems

  • Rewriting equations to interpret features (e.g. maximum profit, minimum cost)

  • Exploring multiple transformations in modelling scenarios

  • Introduction to piecewise models for hybrid systems

Units 1 & 2 (Methods, Transformations)
Focus on understanding algebraic and geometric transformations of functions, including linear, quadratic, and other polynomial forms. Emphasis is placed on domain/range, graphical representations, and algebraic rules governing transformations. These units also cover foundational skills for analyzing functions and modelling real-world scenarios.

Unit 1: Algebraic and Graphical Foundations

1.1 Introduction to Functions and Notation

  • Definition of a function

  • Function notation and evaluation

  • Domain and range (set notation and inequalities)

1.2 Linear and Quadratic Functions

  • Forms of linear functions: gradient-intercept, point-slope

  • Quadratics in standard, factored, and vertex form

  • Techniques for graphing from algebraic form

  • Axis of symmetry, vertex, and intercepts

1.3 Transformations of the Plane

  • Translations: horizontal and vertical shifts

  • Reflections: across the x-axis and y-axis

  • Dilations: vertical and horizontal stretches/compressions

  • Combined (composite) transformations

  • Impact on graphs and equations

  • Identifying transformations from graphs and equations

1.4 Modelling with Functions

  • Using linear and quadratic models in applied contexts

  • Interpretation of parameters (slope, intercept, vertex)

  • Fitting models to data (by hand and with technology)

Unit 2: Further Transformations and Graphical Reasoning

2.1 General Function Transformations

  • Algebraic rules for y = af(b(x + c)) + d

  • Interpretation of parameters a, b, c, and d

  • Application to polynomial and other non-linear functions

  • Transformation of piecewise and absolute value functions

2.2 Inverse and Composite Functions

  • Definition of inverse functions and notation f⁻¹(x)

  • Finding inverses graphically and algebraically (when they exist)

  • Domain and range considerations

  • Composite functions (f ∘ g)(x), evaluation and domain constraints

2.3 Graph Sketching and Analysis

  • Determining function behavior under transformations

  • Symmetry, intercepts, and turning points

  • Sketching without technology

  • Use of CAS/graphing calculators for verification and modelling

2.4 Real-World Modelling and Problem Solving

  • Applying transformations to contextual problems

  • Rewriting equations to interpret features (e.g. maximum profit, minimum cost)

  • Exploring multiple transformations in modelling scenarios

  • Introduction to piecewise models for hybrid systems

About Author

Methods Tutor

Methods Tutor

Methods Tutor

Theo – Tutor Summary

  • Specialty: Mathematical Methods

  • ATAR: 99.65

  • School: Xavier College Alumni

  • Subject Achievements:


    • 50 Raw in Global Politics

    • 47 Raw in History Revolutions

    • 47 Raw in Mathematical Methods

    • 44 Raw in English

Theo – Tutor Summary

  • Specialty: Mathematical Methods

  • ATAR: 99.65

  • School: Xavier College Alumni

  • Subject Achievements:


    • 50 Raw in Global Politics

    • 47 Raw in History Revolutions

    • 47 Raw in Mathematical Methods

    • 44 Raw in English

Theo – Tutor Summary

  • Specialty: Mathematical Methods

  • ATAR: 99.65

  • School: Xavier College Alumni

  • Subject Achievements:


    • 50 Raw in Global Politics

    • 47 Raw in History Revolutions

    • 47 Raw in Mathematical Methods

    • 44 Raw in English

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Beginner

45:12

Free

Beginner

45:12

Free