Math unit30 functions
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This document contains 6 presentations on functions, mappings, and domains: 1) It introduces functions, mappings, and domains. 2) It further explores functions, mappings, and domains with examples. 3) It provides another example and asks about domain and range. 4) It covers composite functions, finding functions of other functions. 5) It introduces the concept of inverse functions. 6) It gives another example of finding the inverse of a function.
Math unit30 functions
- 1. 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
- 2. Unit 30 30.1 Functions, Mappings and Domains 1
- 3. Example If , use the 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
- 5. Example Complete the mapping diagram 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 ? ?
- 6. Unit 30 30.3 Functions, Mappings and Domains 3
- 7. Example If f is defined 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 Composite Functions
- 9. The concept of a 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 Inverse Functions 1
- 11. 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.
- 12. Unit 30 30.6 Inverse Function 2
- 13. For functions that are 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