1. www.le.ac.uk Introduction to functions Department of Mathematics University of Leicester

2. Content FunctionsIntroductionFunctions as graphsWorking with functionsMappings

3. Introduction Functions Mappings Functions as graphs Working with functions Next Intro

4. Mappings Next Functions Mappings Functions as graphs Working with functions Intro

5. Domain & Range Next Functions Mappings Functions as graphs Working with functions Intro

6. Functions Next Functions Mappings Functions as graphs Working with functions Intro

7. One-to-one A mapping that maps one element to one element is called a one-to-one function. Next Functions Mappings Functions as graphs Working with functions Intro

8. Many-to-one A mapping that maps more than one element to one element is called a many-to-one function. Next Functions Mappings Functions as graphs Working with functions Intro

9. One-to-many A mapping that maps one element to one or more elements is not a function. Next Functions Mappings Functions as graphs Working with functions Intro

10. Question... Which of these is a many-to-one function? None of the above Functions Mappings Functions as graphs Working with functions Intro

11. Question... What is this: ? One-to-One One-to-ManyMany-to-One Functions Mappings Functions as graphs Working with functions Intro

12. Question... What is this: ? One-to-One One-to-ManyMany-to-One Functions Mappings Functions as graphs Working with functions Intro

13. Working with functions Next Functions Mappings Functions as graphs Working with functions Intro

14. Examples Next Functions Mappings Functions as graphs Working with functions Intro

15. Your turn 3 8 9 27 None of the above Functions Mappings Functions as graphs Working with functions Intro

16. Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

17. Functions as graphs Domain Range Next Functions Mappings Functions as graphs Working with functions Intro

18. Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

19. Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

20. Functions as graphs Next Functions Mappings Functions as graphs Working with functions Intro

21. Question... Functions Mappings Functions as graphs Working with functions Intro What kind of mapping is this? One-to-0neOne-to-manyMany-to-one

22. Conclusion Functions Mappings Functions as graphs Working with functions Next Intro You should now be able to: Find the range and domain of a mapping. Categorise mappings (one-to-one, etc.) Do simple computations with functions. When you feel comfortable move on to composition of functions.