Overview remaining weeks

Thur, 19/6 : Functions (3A)Tue, 24/06 : Sports day(no lesson)Wed, 25/06 : Functions (3BC – mainly revision)Tue, 01/07 : Functions (3D)Wed, 02/07 : Functions (3E)Tue, 08/07 : Functions revisionWed, 09/07 : Test (Functions and Calculus)Tue, 15/07 : presentationsWed, 16/07 : presentations

C3 (Ch 3) FUNCTIONS

Task 1: Come up with a definition for a function

1. Individually: Spend 1mins on your own thinking about key words, concepts taking notes of your ideas

2. Share with your partner and come up with your joint definition

Aim: Defining functions using the concept of mappingsExample: Pets owned by children in a particular street

Input : Domain: 4 children who live in a particular street

Use this example to clarify terminology:

Possible Outcome: Co-domain is the set of all possible pets

Actual Output : Range is {dog, cat, rabbit, fish} since only these four different types of pet are owned by this particular set of children

Use this example to clarify terminology:

Domain: 4 mums at a toddler groupCo-domain is children present at this groupRange same as co-domain since co-domain is defined as children present at this group rather than all children

Use this example to clarify terminology:

Domain: 6 children who live in a particular streetCo-domain allowed ages for toddler group(up to 4years)Range is {0,1,3,4} since there is no 2year old in this particular group

How could you classify different types of mappings?

There are four types of possible mappings:

“one – to – one”

“one – to – many”

“many – to – one”

“many – to – many”

A function is a special type of mapping such that each member of the domain is mapped to one, and only one, element in the co-domain.DOMAINThe DOMAIN is the set of ALLOWED INPUTS TO A FUNCTION.CO-DOMAINThe Co-domain is the set of POSSIBLE OUTPUTS FROM A FUNCTIONRANGEThe range is a subset of the codomain, it is the set of ACTUAL OUTPUTS

More terminology:

This is a ………………. mapping.

For every value of x, there is one value of 1 – 3x, and no two objects map to the same image.

The co-domain and the range is also Q, since all rational numbers are the image of another rational number under this mapping.

This mapping is also a function as there is only one possible image for each object.

MEI link

Practice/Homework: 3A:1, 4, 5

FUNCTIONS NOT FUNCTIONS

One-onemapping

Many-onemapping

One-Manymapping

Many-Manymapping

     

     

3y x 1yx

2 3y x 2 2

14 9x y

y x 4y x3y x 3y x

Place the following mappings in the table

FUNCTIONS (nearly!) NOT FUNCTIONS

One-onemapping

Many-onemapping

One-Manymapping

Many-Manymapping

     

     

3y x 1yx

2 3y x

y x

4y x3y x

3y x

Place the following mappings in the table

2 2

14 9x y