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**Unformatted text preview: **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 + 20 656 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....

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