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**Unformatted text preview: **Section 7.1 Introducing Rational Functions 615 Version: Fall 2007 7.1 Exercises In Exercises 1- 14 , perform each of the following tasks for the given rational func- tion. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. ii. Use geometric transformations as in Examples 10, 12, and 13 to draw the graphs of each of the following ra- tional functions. Draw the vertical and horizontal asymptotes as dashed lines and label each with its equa- tion. You may use your calculator to check your solution, but you should be able to draw the rational function without the use of a calculator. iii. Use set-builder notation to describe the domain and range of the given rational function. 1. f ( x ) =- 2 /x 2. f ( x ) = 3 /x 3. f ( x ) = 1 / ( x- 4) 4. f ( x ) = 1 / ( x + 3) 5. f ( x ) = 2 / ( x- 5) 6. f ( x ) =- 3 / ( x + 6) 7. f ( x ) = 1 /x- 2 8. f ( x ) =- 1 /x + 4 9. f ( x ) =- 2 /x- 5 10. f ( x ) = 3 /x- 5 11. f ( x ) = 1 / ( x- 2)- 3 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 12. f ( x ) =- 1 / ( x + 1) + 5 13. f ( x ) =- 2 / ( x- 3)- 4 14. f ( x ) = 3 / ( x + 5)- 2 In Exercises 15- 22 , find all vertical as- ymptotes, if any, of the graph of the given function. 15. f ( x ) =- 5 x + 1- 3 16. f ( x ) = 6 x + 8 + 2 17. f ( x ) =- 9 x + 2- 6 18. f ( x ) =- 8 x- 4- 5 19. f ( x ) = 2 x + 5 + 1 20. f ( x ) =- 3 x + 9 + 2 21. f ( x ) = 7 x + 8- 9 22. f ( x ) = 6 x- 5- 8 In Exercises 23- 30 , find all horizontal asymptotes, if any, of the graph of the given function. 23. f ( x ) = 5 x + 7 + 9 24. f ( x ) =- 8 x + 7- 4 616 Chapter 7 Rational Functions Version: Fall 2007 25. f ( x ) = 8 x + 5- 1 26. f ( x ) =- 2 x + 3 + 8 27. f ( x ) = 7 x + 1- 9 28. f ( x ) =- 2 x- 1 + 5 29. f ( x ) = 5 x + 2- 4 30. f ( x ) =- 6 x- 1- 2 In Exercises 31- 38 , state the domain of the given rational function using set- builder notation. 31. f ( x ) = 4 x + 5 + 5 32. f ( x ) =- 7 x- 6 + 1 33. f ( x ) = 6 x- 5 + 1 34. f ( x ) =- 5 x- 3- 9 35. f ( x ) = 1 x + 7 + 2 36. f ( x ) =- 2 x- 5 + 4 37. f ( x ) =- 4 x + 2 + 2 38. f ( x ) = 2 x + 6 + 9 In Exercises 39- 46 , find the range of the given function, and express your an- swer in set notation. 39. f ( x ) = 2 x- 3 + 8 40. f ( x ) = 4 x- 3 + 5 41. f ( x ) =- 5 x- 8- 5 42. f ( x ) =- 2 x + 1 + 6 43. f ( x ) = 7 x + 7 + 5 44. f ( x ) =- 8 x + 3 + 9 45. f ( x ) = 4 x + 3- 2 46. f ( x ) =- 5 x- 4 + 9 Section 7.1 Introducing Rational Functions Version: Fall 2007 7.1 Solutions 1. Start with the graph of y = 1 /x in (a). Multiplying by 2 produces the equation y = 2 /x and stretches the graph vertically by a factor of 2 as shown in (b). Multiplying by- 1 produces the equation y =- 2 /x and reflects the graph of y = 2 /x in (b) over the x-axis to produce the graph of y =- 2 /x in (c)....

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