Contents
Introduction
The Language of Functions
 Mapping: An operation that associates each element of a given set (the domain) with one or more elements of a second set (the range).
But what does this really mean? Well in short, a mapping is a rule which shows you how to get from an input to an output. This can cover a whole range of things.
e.g.
MAPPING: Take the input, and add 4.
INPUT: 1
OUTPUT: 5
or
INPUT: 7
OUTPUT: 11
Mappings can be shown by using a diagram, here is one for the example mapping mentioned above:
 Domain: All the possible input values for your mapping (for a function, your x values).
 Range: All the possible output values for your mapping (for a function, your y values).
All the functions you've come across before in maths are examples of mappings.
You have an input (your x values), and you have a rule which tells you what to do in order to get to your output (your y values)!
But does that mean all mapping are functions?
NO!
There are four types of mappings. Two of which ARE functions, but the other two certainly aren't!
Types of Mapping
As forementioned mappings come in four different flavors.
 Onetoone
 Onetomany
 Manytoone
 Manytomany
This sort of mapping has only one possible output for any given input. And each input has a unique output. For example the mapping in figure 1 is an example of a onetoone mapping.
Transformations
Transformations General case:

Lets take f(x) as our original function and discover how changes to the function result in graphic transformations.
 Stretches:
Stretches parallel to both the x and y axes can be represented by transformations:
This represents a stretch parallel to the y axis, scale factor C.
This represents a stretch parallel to the x axis, scale factor 1/C.
Composite Functions
blah blah blah
Inverse Functions
blah blah blah
Inverse Trigonometric Functions
I find spider diagrams useful to revise from, so I made some. Feel free to use them for your revision!
Even, odd and Periodic Functions
I find spider diagrams useful to revise from, so I made some. Feel free to use them for your revision!
The Modulus Function
I find spider diagrams useful to revise from, so I made some. Feel free to use them for your revision!