UNIT OVERVIEW

This unit covers functions — one of the most important topics in mathematics. Functions help us describe and predict patterns in the world around us.

A function is a rule that takes an input and gives exactly one output. Think of it as a machine: put in a number, follow the rule, and get one answer out.

In this unit, you will learn:

• What makes a relationship a function (the "one input, one output" rule)
• How to represent functions using tables, graphs, words, and formulae
• The shapes and properties of linear, quadratic, hyperbolic, and exponential functions
• How to identify key features: domain, range, intercepts, asymptotes, turning points, and axes of symmetry
• How parameters $a$ and $q$ transform basic graphs
• How to sketch and interpret $y = \sin\theta$, $y = \cos\theta$, and $y = \tan\theta$
• How to find equations from graphs and apply functions to real-world problems

Real-Life Examples of Functions

1. Cell phone data costs: If data costs R99 per GB, then $\text{Cost} = 99 \times \text{GB used}$ is a linear function.