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

• Notes
• davidvictor
• 48
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–6. Sign up to view the full content.

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: 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

This preview has intentionally blurred sections. Sign up to view the full version.

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 617 Version: Fall 2007 7.1 Answers 1. D = { x : x = 0 } , R = { y : y = 0 } x 10 y 10 y =0 x =0 3. D = { x : x = 4 } , R = { y : y = 0 } x 10 y 10 y =0 x =4 5. D = { x : x = 5 } , R = { y : y = 0 } x 10 y 10 y =0 x =5 7. D = { x : x = 0 } , R = { y : y = - 2 } x 10 y 10 y = - 2 x =0 9. D = { x : x = 0 } , R = { y : y = - 5 } x 10 y 10 y = - 5 x =0 11. D = { x : x = 2 } , R = { y : y = - 3 } x 10 y 10 y = - 3 x =2

This preview has intentionally blurred sections. Sign up to view the full version.

618 Chapter 7 Rational Functions Version: Fall 2007 13. D = { x : x = 3 } , R = { y : y = - 4 } x 10 y 10 y = - 4 x =3 15. Vertical asymptote: x = - 1 17. Vertical asymptote: x = - 2 19. Vertical asymptote: x = - 5 21. Vertical asymptote: x = - 8 23. Horizontal asymptote: y = 9 25. Horizontal asymptote: y = - 1 27. Horizontal asymptote: y = - 9 29. Horizontal asymptote: y = - 4 31. Domain = { x : x = - 5 } 33. Domain = { x : x = 5 } 35. Domain = { x : x = - 7 } 37. Domain = { x : x = - 2 } 39. Range = { y : y = 8 } 41. Range = { y : y = - 5 } 43. Range = { y : y = 5 } 45. Range = { y : y = - 2 }
Section 7.2 Reducing Rational Functions 633 Version: Fall 2007 7.2 Exercises In Exercises 1 - 12 , reduce each rational number to lowest terms by applying the following steps: i. Prime factor both numerator and de- nominator. ii. Cancel common prime factors. iii. Simplify the numerator and denomi- nator of the result.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern