Lecture 12
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The document covers functions and their properties including definitions, examples, graphs, and exercises. It discusses functions, function notation, arrow diagrams, ranges, vertical line tests, binary operations, and examples of determining whether relations are functions or not. Solutions and explanations are provided for exercises on identifying functions from graphs or equations.
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Lecture 12
- 1. Functions – (15 - 2)
- 2. Functions – (15 – 2a)
- 3. Example – (15 - 3)
- 4. Solution – (15 – 3a)
- 5. Solution – (15 – 3b)
- 6. Solution – (15 – 3c)
- 7. Function – (15 - 5)
- 8. Remarks – (15 – 5a)
- 9. Arrow Diagram of a Function – (15 - 6)
- 10. Example – (15 – 6a)
- 11. Example – (15 – 6b)
- 12. Nonfunction – (15 - 7)
- 13. Range of a Function – (15 - 8)
- 14. Remarks – (15 – 8a)
- 15. Exercise – (15 - 9)
- 16. Exercise – (15 – 9a)
- 17. Solution – (15 – 9b)
- 18. Graph of a Function – (11 - 11)
- 19. Graph of a Function – (15 – 11a)
- 20. Graph of a Function – (15 – 11b)
- 21. Vertical Line Test – (15 - 12)
- 22. Example – (15 - 13)
- 23. Solution – (15 – 13a)
- 24. Solution – (15 – 13b)
- 25. Exercise – (15 - 15)
- 26. Exercise – (15 – 15a)
- 27. Exercise – (15 – 15b)
- 28. Exercise – (15 - 17)
- 29. Exercise – (15 – 17a)
- 30. Exercise – (15 – 17b)
- 31. Exercise – (15 - 18)
- 32. Solution – (15 – 18a)
- 33. Functions Not Well Defined – (15 - 20)
- 34. Solution – (15 – 20a)
- 35. Solution – (15 – 20b)
- 36. Exercise – (15 - 21)
- 37. Solution – (15 – 21a)
- 38. Solution – (15 - 22)
- 39. Binary Operations – (15 - 28)
- 40. Example – (15 – 28a)