Overview remaining weeks
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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
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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
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Aim: Defining functions using the concept of mappingsExample: Pets owned by children in a particular street
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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
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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
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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?
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There are four types of possible mappings:
“one – to – one”
“one – to – many”
“many – to – one”
“many – to – many”
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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
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More terminology:
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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.
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Practice/Homework: 3A:1, 4, 5
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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
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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
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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)
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TopTip:If you are asked to state the range of a given function, you should............
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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
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Homework(due next Wed!): 3B: 1, 4 & 3C: 1, 5, 7*
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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
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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
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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
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www.supermathsworld.com
How would you summarise today’s lesson to someone who has missed it?