Unit 30 Functions Presentation 1 Functions, Mappings and Domains 1

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Presentation transcript:

Unit 30 Functions Presentation 1 Functions, Mappings and Domains 1 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

30.1 Functions, Mappings and Domains 1 Unit 30 30.1 Functions, Mappings and Domains 1

Example If , use the mapping diagram below to show how v maps to p for . Consider integer values of v. Solution 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 Extension Question What is the range for p? Is this 1:1 mapping? Yes ? ? v (domain for p) p

30.2 Functions, Mapping and Domains 2 Unit 30 30.2 Functions, Mapping and Domains 2

Complete the mapping diagram below for the function Example Complete the mapping diagram below for the function Consider integer values of x. Solution 25 20 15 10 5 5 4 3 2 1 -1 -2 -3 -4 -5 Extension Questions What is the range for y? Is this 1:1 mapping? No ? ?

30.3 Functions, Mappings and Domains 3 Unit 30 30.3 Functions, Mappings and Domains 3

If f is defined by; for all ,what are the values of: (a) (b) (c) (d) Example If f is defined by; for all ,what are the values of: (a) (b) (c) (d) Extension Question What is the range of f ? Sketch the function; Solution (a) (b) (c) (d) ? ? ? ? ? ? ? y ? ? ? ? ? ? x -2 -1 1 2 The function f is not a 1:1 mapping. Explain why not? all map to 0 ?

Unit 30 30.4 Composite Functions

The concept of a function of a function is introduced here. Example The functions of f and g are defined by Find and What are the values of and Solution (a) (b) ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Unit 30 30.5 Inverse Functions 1

If , we can 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.

Unit 30 30.6 Inverse Function 2

If , find it’s inverse function. Solution For functions that are 1:1 mappings, we can find their inverse functions. Example If , find it’s inverse function. Solution Let and find x as a function of y. i.e. Check ? ? ? ? ? ? ? ? ? ? ? ?