Functions: Definitions, Notation & Terminology

We learn what a function is, how it works and how to calculate the "output" value it produces when an "input" value is placed inside it. The term "mapping" is introduced as well as the terms "domain" and "range".

Curve of a Function

We learn how to use a table of values to calculate the coordinates of points the function's curve passes through in order to draw its curve.

Plotting Curves with Graphical Calculator

We learn how to use the Graphical Display Calculator (GDC) to plot a function's curve.

Domain & Range of a Function 
We learn how to find the domain and the range of a function by looking at its curve 
Domain of a Function 
Given a function's equation, we learn how to find its domain algebraically. 
Vertical Line Test

How to check whether a curve represents a function \(f(x)\), simply by drawing a vertical line.

Mappings & Horizontal Line Test

We define onetoone and manytoone mappings and learn a graphical method for checking whether a mapping is onetoone or manytoone mapping.

Composite Functions

Given two functions \(f(x)\) and \(g(x)\) we learn how to find the expressions for the composite functions \(f\begin{pmatrix}g(x)\end{pmatrix}\) and \(g\begin{pmatrix}f(x)\end{pmatrix}\) as well as how to find the domain and range of composite functions.

Inverse Functions

Given a function \(f(x)\), we learn how to find its inverse function, \(f^{1}(x)\).
