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 : Functions revisionTue, 15/07 : Test (Functions and Calculus)Wed, 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

Starter: Pick one of the key words/key aspects of last lesson and explain it to the class! (You get 2 mins to look at your notes from last lesson)

TopTip:If you are asked to state the range of a given function, you should............

Practice: State the range of ....

1) f(x) = x2, x є R2) f(x) = 3x2, x є R

3) f(x) = x2 +1, x є R

4) f(x) = (x + 1)2, x є R

5) f(x) = (x -1)2+ 3, x є R

6) f(x) = x2+6x +9, x є R7) f(x) = x2 + 6x + 11, x є R

Summarise, then P25-35 : revise transformations

Homework(due next Wed!): 3B: 1, 4 & 3C: 1, 5, 7*

Starter: Work out the effect of the combined transformations

http://www.mymaths.co.uk/tasks/library/alevel/lib/loadLesson.asp?title=alevel/core3/Functions/functions5Transform&taskID=2142

In the same way we can combine transformations, we can also combine functions, which we call composite functions:

E.g. fg(x) means first apply the function g to x, then apply the function f to the result. The important thing to remember is to follow the order:

Practice: Composite functions sheet

Now try these: Find f(g(x)) for each pair of functions f and g as defined:

a) f(x) = x + 1 g(x) = x – 1

b) f(x) = 3x g(x) = 0.5x

c) f(x) = x3 g(x) = x 1/3

What do you notice?

http://www.mymaths.co.uk/tasks/library/alevel/lib/loadLesson.asp?title=alevel/core3/Functions/functions1Functions&taskID=2138

Practice: 3D: Q2, 3

www.supermathsworld.com

How would you summarise today’s lesson to someone who has missed it?