Math unit30 functions

Math unit30 functions

• 1.
  Unit 30 Functions Presentation 1Functions, Mappings and Domains 1 Presentation 2 Functions, Mapping and Domains 2 Presentation 3 Functions, Mapping and Domains 3 Presentation 4 Composite Functions Presentation 5 Inverse Functions 1 Presentation 6 Inverse Functions 2
• 2.
  Unit 30 30.1 Functions,Mappings and Domains 1
• 3.
  Example If , usethe mapping diagram below to show how v maps to p for . Consider integer values of v. 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 Solution Extension Question What is the range for p? Is this 1:1 mapping? Yes ? ? v (domain for p) p
• 4.
  Unit 30 30.2 Functions,Mapping and Domains 2
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  Example Complete the mappingdiagram below for the function Consider integer values of x. 5 4 3 2 1 0 -1 -2 -3 -4 -5 25 20 15 10 5 0 Solution Extension Questions What is the range for y? Is this 1:1 mapping? No ? ?
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  Unit 30 30.3 Functions,Mappings and Domains 3
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  Example If f isdefined by; for all ,what are the values of: (a) (b) (c) (d) Solution (a) (b) (c) (d) ? ? ? ? ? ? ? ? ? ? ? ? Extension Question What is the range of f ? Sketch the function; ? x y 2-2 -1 1 The function f is not a 1:1 mapping. Explain why not? all map to 0?
• 8.
  Unit 30 30.4 CompositeFunctions
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  The concept ofa function of a function is introduced here. Example The functions of f and g are defined by (a)Find and (b)What are the values of and Solution (a) (b) ???? ?? ? ? ?? ????
• 10.
  Unit 30 30.5 InverseFunctions 1
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  If , wecan make C the subject of the equation by writing or We say that F and C are inverse functions. For inverse functions, f and g, then Example Show that if then Solution ??? ? ? Note: We write or to mean ,etc.
• 12.
  Unit 30 30.6 InverseFunction 2
• 13.
  For functions thatare 1:1 mappings, we can find their inverse functions. Example If , find it’s inverse function. Solution ? ? ? ? ? ? ? ? ? ? ? ? i.e. Let and find x as a function of y. Check