Introduction to Functions Core 3 Chapter 1

Alain Graham
Note by Alain Graham, updated more than 1 year ago
Alain Graham
Created by Alain Graham over 3 years ago
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Notes on classwork valid for the AQA exam in 2018.

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Page 1

Introduction to functions 1

There are two types of functions; One-To-One functions and Many-To-One

One-To-One Functions

The substitution of any given number that gives the answer that is independent of any other number in that function. 3x-1=y If x=1 and x=-1 x=1; 3(1)-1=y y=2 x=-1 3(-1)-1=y y=-4 THIS IS A ONE-TO-ONE FUNCTION

Many-To-One Functions

The substitution of different values, of which give the same answer. For Example: 3x^4=y when x=1 and x=-1 so when x=1 3(1)^4=y y=3 AND when x=-1 3(-1)^4=y  

So with that in mind (source: My Resource: https://www.goconqr.com/en-GB/p/9367691) y=3 THIS IS A MANY-TO-ONE FUNCTION

Page 2

Introduction to functions 1 part 2

In order for a function to exist, however, the domain must be defined or the values of which can't be in the domain must be identified.

Domains

The mapping becomes a function when the domain has been identified, this can be written in interval notation [[number ie -1],∞) or as an inequality ie x≥1 or x≠0   So the graph indicating F(x)=-x^2 that has the domain x>2 creates this graph

and the answer for finding the range would be F(x)<-4.   If we didn't add the  domain the plotted graph would look like this:

Revise tip 1 - Use Flashcards

Here are some to start you off. Feel free to edit them and add your own example. Don't forget to message me so I can have a look at them and add a link below:

Page 3

Introduction to functions 2

As to regards to what we said in the previous page their are two types of graphical equations that ARE NOT FUNCTIONS. These are One-To-Many Graphs and Many-To-Many Graphs

We need not delve further for core 3 examinations TBC

Page 4

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