Unit 30 Functions Presentation 1 Functions Mappings and

Unit 30 Functions Presentation 1 Functions, 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

Unit 30 30. 1 Functions, Mappings and Domains 1

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

Unit 30 30. 2 Functions, Mapping and Domains 2

Example Complete the mapping diagram below for the function Consider integer values of x. Solution 5 25 Extension Questions 4 3 20 What is the range for y? 15 Is this 1: 1 mapping? 2 1 0 -1 10 -2 -3 5 -4 -5 0 ? No ?

Unit 30 30. 3 Functions, Mappings and Domains 3

Example If f is defined by; for all (a) (b) (c) Extension Question Solution What is the range of f ? ? (a) ? ? ? (b) Sketch the function; ? ? (c) ? (d) ? ? ? , what are the values of: (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 is introduced here. Example The functions of f and g are defined by (a) Find and (b) What are the values of Solution (a) and (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 Solution Show that if ? ? then ? ? ? Note: We write or to mean , etc.

Unit 30 30. 6 Inverse Function 2

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