# Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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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: 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 -→ ?

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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 ) = ? . 44. Given that h takes a real number, doubles it, adds 5, then takes the square root of the result, then h ( x ) = ? . In Exercises 45 - 54 , evaluate the given function at the given value b . 45. f ( x ) = 12 x + 2 for b = 6 . 46. f ( x ) = - 11 x - 4 for b = - 3 . 47. f ( x ) = - 9 x - 1 for b = - 5 . 48. f ( x ) = 11 x + 4 for b = - 4 .
Section 2.1 Introduction to Functions 89 Version: Fall 2007 49. f ( x ) = 4 for b = - 12 . 50. f ( x ) = 7 for b = - 7 . 51. f ( x ) = 0 for b = - 7 . 52. f ( x ) = 12 x + 8 for b = - 3 . 53. f ( x ) = - 9 x + 3 for b = - 1 . 54. f ( x ) = 6 x - 3 for b = 3 . In Exercises 55 - 58 , given that the func- tion f is defined by the rule f ( x ) = 2 x + 7 , determine where the input number is mapped.

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• Graph of a function, vertical line test, Vertical Geometric Transformations

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