Course: Year 12 Mathematics Advanced

Functions and Graphing Techniques

A structured pathway through function notation, domain and range, transformations, graph features, exponential and logarithmic graphing, absolute value functions, inverse functions, graphical solving, and modelling skills for Year 12 Mathematics Advanced.

Active lessons

11

Planned lessons

11

Lesson sequence

Learn -> Guided Practice -> Independent Practice -> Mastery Quiz

How to use this unit

  • Start with domain, range, and function notation.
  • Use mastery quizzes to check whether each skill is secure.
  • If you miss the pass mark, work through the full staged lesson.
  • Return to graphing basics before tackling transformations or modelling questions.

What this unit covers

Function notation
Domain and range
Graph transformations
Reflections, stretches, and translations
Intercepts and key features
Asymptotes and reciprocal-style graphs
Exponential and logarithmic graphs
Absolute value functions
Inverse functions
Graphical equations and inequalities
Modelling with functions
Mixed exam practice

Unit pathway

Lesson pathway

11 of 11 active

1

Lesson 1

Domain, range, and function notation

Use function notation and identify domain and range from equations, graphs, and contexts.

Active
2

Lesson 2

Graph transformations

Describe translations, reflections, and dilations using function notation.

Active
3

Lesson 3

Reflections, Stretches, and Translations

Combine reflections, dilations, and translations when sketching transformed functions.

Active
4

Lesson 4

Intercepts and Key Features

Identify intercepts, turning points, symmetry, and other features needed for accurate graph sketches.

Active
5

Lesson 5

Asymptotes and Reciprocal-Style Graphs

Recognise and sketch graphs with vertical and horizontal asymptotes.

Active
6

Lesson 6

Solving Equations and Inequalities Graphically

Use graphs to solve equations, inequalities, and compare functions.

Active
7

Lesson 7

Modelling with Functions

Use functions and graphs to model and interpret real-world relationships.

Active
8

Lesson 8

Mixed Functions and Graphing Exam Practice

Practise mixed exam-style questions involving function notation, transformations, features, asymptotes, and graphical solving.

Active
9

Lesson 9

Exponential and Logarithmic Graphs in Graphing Techniques

Identify transformations, asymptotes, intercepts, domain, and range for exponential and logarithmic graphs.

Active
10

Lesson 10

Absolute Value Functions

Interpret absolute value transformations, graph features, equations, domain and range.

Active
11

Part of the Online Learning Package

This unit is part of the Nova Maths online learning package. The lesson pathway is available for preview, and full access requires an active online learning subscription.

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