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**Unformatted text preview: **Section 2.1 Introduction to Functions 87 Version: Fall 2007 2.1 Exercises In Exercises 1- 6 , state the domain and range of the given relation. 1. R = { (1 , 3) , (2 , 4) , (3 , 4) } 2. R = { (1 , 3) , (2 , 4) , (2 , 5) } 3. R = { (1 , 4) , (2 , 5) , (2 , 6) } 4. R = { (1 , 5) , (2 , 4) , (3 , 6) } 5. x 5 y 5 6. x 5 y 5 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 In Exercises 7- 12 , create a mapping di- agram for the given relation and state whether or not it is a function. 7. The relation in Exercise 1 . 8. The relation in Exercise 2 . 9. The relation in Exercise 3 . 10. The relation in Exercise 4 . 11. The relation in Exercise 5 . 12. The relation in Exercise 6 . 13. Given that g takes a real number and doubles it, then g : x-→ ? . 14. Given that f takes a real number and divides it by 3, then f : x-→ ? . 15. Given that g takes a real number and adds 3 to it, then g : x-→ ? . 16. Given that h takes a real number and subtracts 4 from it, then h : x-→ ? . 17. Given that g takes a real number, doubles it, then adds 5, then g : x-→ ? . 18. Given that h takes a real number, subtracts 3 from it, then divides the re- sult by 4, then h : x-→ ? . Given that the function f is defined by the rule f : x-→ 3 x- 5 , determine where the input number is mapped in Exercises 19- 22 . 19. f : 3-→ ? 88 Chapter 2 Functions Version: Fall 2007 20. f :- 5-→ ? 21. f : a-→ ? 22. f : 2 a + 3-→ ? Given that the function f is defined by the rule f : x-→ 4- 5 x , determine where the input number is mapped in Exercises 23- 26 . 23. f : 2-→ ? 24. f :- 3-→ ? 25. f : a-→ ? 26. f : 2 a + 11-→ ? Given that the function f is defined by the rule f : x-→ x 2- 4 x- 6 , deter- mine where the input number is mapped in Exercises 27- 30 . 27. f : 1-→ ? 28. f :- 2-→ ? 29. f :- 1-→ ? 30. f : a-→ ? Given that the function f is defined by the rule f : x-→ 3 x- 9 , determine where the input number is mapped in Exercises 31- 34 . 31. f : a-→ ? 32. f : a + 1-→ ? 33. f : 2 a- 5-→ ? 34. f : a + h-→ ? Given that the functions f and g are de- fined by the rules f : x-→ 2 x + 3 and g : x-→ 4- x , determine where the in- put number is mapped in Exercises 35- 38 . 35. f : 2-→ ? 36. g : 2-→ ? 37. f : a + 1-→ ? 38. g : a- 3-→ ? 39. Given that g takes a real number and triples it, then g ( x ) = ? . 40. Given that f takes a real number and divides it by 5, then f ( x ) = ? . 41. Given that g takes a real number and subtracts it from 10, then g ( x ) = ? . 42. Given that f takes a real number, multiplies it by 5 and then adds 4 to the result, then f ( x ) = ? . 43. Given that f takes a real number, doubles it, then subtracts the result from 11, then f ( x ) = ? ....

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