Functions and Other Graphs

Nine lessons that build the language senior mathematics is written in. Each definition here earns the notation that follows it: relations make functions meaningful, the function condition makes function notation possible, and domain and range make every later graph readable.

9lessons

14syllabus points

6-7hstudy

Start Lesson 1 →

Relations, functions and notation

Relations and Ordered Pairs

Any association between two sets, written four equivalent ways

›

What Makes a Relation a Function

One input, one output, and the vertical line test as that rule drawn

›

Function Notation

Name, variable and output in four characters, and when to substitute or solve

›

Domain, range and transformations

Domain

Start from everything and remove what breaks: two exclusions, three notations

›

Range

Read it up the vertical axis, and why it is harder than the domain

›

Domain and Range of Common Functions

Six shapes worth knowing on sight, and the one question separating them

›

Transforming Function Graphs

Inside moves the domain, outside moves the range, and no formula is needed

›

Inequalities and regions

Inequalities in One Variable

The one rule about negatives, and open against filled circles

›

Regions in Two Variables

Boundary, line style and one test point; then systems and their corners

›

Focus Area Snapshot

9lessons

14syllabus points

27worked examples

72questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Advanced in Year 11. Almost nothing here is ever retired: function notation, domain and range, and the transformation rules are used unchanged for the whole of senior mathematics, and the transformation rules apply to every function you will meet, not only the ones in this area.

Start Lesson 1 →