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Overview remaining weeks

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 revision Wed, 09/07 : Functions revision

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Overview remaining weeks

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  1. 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 revision Wed, 09/07 : Functions revision Tue, 15/07 : Test (Functions and Calculus) Wed, 16/07 : presentations

  2. C3 (Ch 3) FUNCTIONS Task 1: Come up with a definition for a function Individually: Spend 1mins on your own thinking about key words, concepts taking notes of your ideas Share with your partner and come up with your joint definition

  3. Aim: Defining functions using the concept of mappings Example: Pets owned by children in a particular street

  4. Use this example to clarify terminology: Input : Domain: 4 children who live in a particular street Possible Outcome: Co-domainis the set of all possible pets Actual Output : Rangeis {dog, cat, rabbit, fish} since only these four different types of pet are owned by this particular set of children

  5. Use this example to clarify terminology: Domain: 4 mums at a toddler group Co-domain is children present at this group Range same as co-domain since co-domain is defined as children present at this group rather than all children

  6. Use this example to clarify terminology: Domain: 6 children who live in a particular street Co-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?

  7. There are four types of possible mappings: “one – to – one” “one – to – many” “many – to – one” “many – to – many”

  8. 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. DOMAIN The DOMAIN is the set of ALLOWED INPUTS TO A FUNCTION. CO-DOMAIN The Co-domainis the set of POSSIBLE OUTPUTS FROM A FUNCTION RANGE The range is a subset of the codomain, it is the set of ACTUAL OUTPUTS

  9. More terminology:

  10. 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.

  11. MEI link

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

  13. Place the following mappings in the table

  14. Place the following mappings in the table

  15. 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)

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

  17. Practice: State the range of .... 1) f(x) = x2, x є R 2) 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 R 7) f(x) = x2 + 6x + 11, x є R Summarise, then P25-35 : revise transformations

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

  19. 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

  20. 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

  21. 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 – 1b) f(x) = 3x g(x) = 0.5xc) f(x) = x3 g(x) = x 1/3What 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

  22. www.supermathsworld.com How would you summarise today’s lesson to someone who has missed it?

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