Chap7 Section3

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

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Section 7.3 Graphing Rational Functions 655 Version: Fall 2007 7.3 Exercises For rational functions Exercises 1 - 20 , follow the Procedure for Graphing Ratio- nal Functions in the narrative, perform- ing each of the following tasks. For rational functions Exercises 1 - 20 , perform each of the following tasks. i. Set up a coordinate system on graph paper. Label and scale each axis. Re- member to draw all lines with a ruler. ii. Perform each of the nine steps listed in the Procedure for Graphing Ratio- nal Functions in the narrative. 1. f ( x ) = ( x 3) / ( x + 2) 2. f ( x ) = ( x + 2) / ( x 4) 3. f ( x ) = (5 x ) / ( x + 1) 4. f ( x ) = ( x + 2) / (4 x ) 5. f ( x ) = (2 x 5) / ( x + 1) 6. f ( x ) = (2 x + 5 / (3 x ) 7. f ( x ) = ( x + 2) / ( x 2 2 x 3) 8. f ( x ) = ( x 3) / ( x 2 3 x 4) 9. f ( x ) = ( x + 1) / ( x 2 + x 2) 10. f ( x ) = ( x 1) / ( x 2 x 2) 11. f ( x ) = ( x 2 2 x ) / ( x 2 + x 2) 12. f ( x ) = ( x 2 2 x ) / ( x 2 2 x 8) 13. f ( x ) = (2 x 2 2 x 4) / ( x 2 x 12) 14. f ( x ) = (8 x 2 x 2 ) / ( x 2 x 6) Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 15. f ( x ) = ( x 3) / ( x 2 5 x + 6) 16. f ( x ) = (2 x 4) / ( x 2 x 2) 17. f ( x ) = (2 x 2 x 6) / ( x 2 2 x ) 18. f ( x ) = (2 x 2 x 6) / ( x 2 2 x ) 19. f ( x ) = (4+2 x 2 x 2 ) / ( x 2 +4 x +3) 20. f ( x ) = (3 x 2 6 x 9) / (1 x 2 ) In Exercises 21 - 28 , find the coordinates of the x -intercept(s) of the graph of the given rational function. 21. f ( x ) = 81 x 2 x 2 + 10 x + 9 22. f ( x ) = x x 2 x 2 + 5 x 6 23. f ( x ) = x 2 x 12 x 2 + 2 x 3 24. f ( x ) = x 2 81 x 2 4 x 45 25. f ( x ) = 6 x 18 x 2 7 x + 12 26. f ( x ) = 4 x + 36 x 2 + 15 x + 54 27. f ( x ) = x 2 9 x + 14 x 2 2 x 28. f ( x ) = x 2 5 x 36 x 2 9 x + 20
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656 Chapter 7 Rational Functions Version: Fall 2007 In Exercises 29 - 36 , find the equations of all vertical asymptotes. 29. f ( x ) = x 2 7 x x 2 2 x 30. f ( x ) = x 2 + 4 x 45 3 x + 27 31. f ( x ) = x 2 6 x + 8 x 2 16 32. f ( x ) = x 2 11 x + 18 2 x x 2 33. f ( x ) = x 2 + x 12 4 x + 12 34. f ( x ) = x 2 3 x 54 9 x x 2 35. f ( x ) = 16 x 2 x 2 + 7 x + 12 36. f ( x ) = x 2 11 x + 30 8 x + 48 In Exercises 37 - 42 , use a graphing cal- culator to determine the behavior of the given rational function as x approaches both positive and negative infinity by per- forming the following tasks: i. Load the rational function into the Y= menu of your calculator. ii. Use the TABLE feature of your calcula- tor to determine the value of f ( x ) for x = 10 , 100, 1000, and 10000. Record these results on your homework in ta- ble form. iii. Use the TABLE feature of your calcula- tor to determine the value of f ( x ) for x = 10 , 100 , 1000 , and 10000 . Record these results on your home- work in table form. iv. Use the results of your tabular explo- ration to determine the equation of the horizontal asymptote. 37. f ( x ) = (2 x + 3) / ( x 8) 38. f ( x ) = (4 3 x ) / ( x + 2) 39. f ( x ) = (4 x 2 ) / ( x 2 + 4 x + 3) 40. f ( x ) = (10 2 x 2 ) / ( x 2 4) 41. f ( x ) = ( x 2 2 x 3) / (2 x 2 3 x 2) 42. f ( x ) = (2 x 2 3 x 5) / ( x 2 x 6) In Exercises 43 - 48 , use a purely ana- lytical method to determine the domain of the given rational function. Describe the domain using set-builder notation.
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