Unit 4 – graphing transformations

A 12-lesson unit for Year 11 with resources.

The lessons and sequences in this program of learning are designed to allow students to explore graphical transformations of functions, including reflections, translations, and dilations.

Students will investigate how changes to equations affect graphs within the scope of the Mathematics Advanced course, and determine key features such as domain, range, intercepts, and asymptotes. Students then apply this knowledge to solve a range of problems including those involving direct and inverse variation.

Introduction

Graphing transformations (DOCX 6 MB)

Lesson 1 – piecewise-defined functions

• Piecewise-defined functions (DOCX 7.7 MB)
• Piecewise-defined functions – slide deck (PPTX 3.4 MB)

Lesson 2 – absolute value

• Absolute value (DOCX 7.5 MB)
• Absolute value – slide deck (PPTX 2.2 MB)

Lesson 3 – solving absolute value equations

• Solving absolute value equations (DOCX 6.1 MB)
• Solving absolute value equations – slide deck (PPTX 9.5 MB)

Lesson 4 – reflection

• Reflection (DOCX 8 MB)
• Reflection – slide deck (PPTX 7.4 MB)

Lesson 5 – translations

• Translations (DOCX 6 MB)
• Translations – slide deck (PPTX 3.8 MB)

Lesson 6 – further circles

• Further circles (DOCX 9 MB)
• Further circles – slide deck (PPTX 3.6 MB)

Lesson 7 – further cubic functions

Further cubic functions (DOCX 6.2 MB)

Lesson 8 – dilations (enlargements and reductions)

• Dilations (enlargements and reductions) (DOCX 8.8 MB)
• Dilations (enlargements and reductions) – slide deck (PPTX 2.7 MB)

Lesson 9 – dilations (horizontal and vertical)

• Dilations (horizontal and vertical) (DOCX 9 MB)
• Dilations (horizontal and vertical) – slide deck (PPTX 3. MB)

Lesson 10 – applying graphing transformations

• Applying graphing transformations (DOCX 6.8 MB)
• Applying graphing transformations – slide deck (PPTX 2.8 MB)

Lesson 11 – direct variation

• Direct variation (DOCX 7.6 MB)
• Direct variation – slide deck (PPTX 2.5 MB)

Lesson 12 – inverse variation

• Inverse variation (DOCX 5.8 MB)
• Inverse variation – slide deck (PPTX 2.1 MB)

Assessment tasks

Students apply their understanding of functions and relations by writing equations with domain and range restrictions to model shapes, and design an original logo using mathematical curves. Then they reflect on how mathematics can be used to create visual designs by evaluating the strengths and limitations of their work.

• Graph transformations – assessment task sample solutions (DOCX 6.6 MB)
• Graph transformations – student assessment task (DOCX 5 MB)
• Graph transformations – teacher information (DOCX 3.5 MB)