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

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