Chapter 7 Rational Functions - College of the Redwoods

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656 Chapter 7 Rational Functions In Exercises 29-36, find the equations of all vertical asymptotes. 29. f(x) = x2 − 7x x 2 − 2x 30. f(x) = x2 + 4x − 45 3x + 27 31. f(x) = x2 − 6x + 8 x 2 − 16 32. f(x) = x2 − 11x + 18 2x − x 2 33. f(x) = x2 + x − 12 −4x + 12 34. f(x) = x2 − 3x − 54 9x − x 2 35. f(x) = 16 − x2 x 2 + 7x + 12 36. f(x) = x2 − 11x + 30 −8x + 48 In Exercises 37-42, use a graphing calculator to determine the behavior of the given rational function as x approaches both positive and negative infinity by performing the following tasks: i. Load the rational function into the Y= menu of your calculator. ii. Use the TABLE feature of your calculator to determine the value of f(x) for x = 10, 100, 1000, and 10000. Record these results on your homework in table form. iii. Use the TABLE feature of your calculator to determine the value of f(x) for x = −10, −100, −1000, and −10000. Record these results on your homework in table form. iv. Use the results of your tabular exploration to determine the equation of the horizontal asymptote. 37. f(x) = (2x + 3)/(x − 8) 38. f(x) = (4 − 3x)/(x + 2) 39. f(x) = (4 − x 2 )/(x 2 + 4x + 3) 40. f(x) = (10 − 2x 2 )/(x 2 − 4) 41. f(x) = (x 2 − 2x − 3)/(2x 2 − 3x − 2) 42. f(x) = (2x 2 − 3x − 5)/(x 2 − x − 6) In Exercises 43-48, use a purely analytical method to determine the domain of the given rational function. Describe the domain using set-builder notation. 43. f(x) = x2 − 5x − 6 −9x − 9 44. f(x) = x2 + 4x + 3 x 2 − 5x − 6 45. f(x) = x2 + 5x − 24 x 2 − 3x 46. f(x) = x2 − 3x − 4 x 2 − 5x − 6 47. f(x) = x2 − 4x + 3 x − x 2 48. f(x) = x 2 − 4 x 2 − 9x + 14 Version: Fall 2007
Section 7.3 Graphing Rational Functions 657 7.3 Answers 1. 7. y 10 y 10 (3,0) y=1 x 10 y=0 (−2,0) x 10 x=−2 x=−1 x=3 3. 9. y 10 y 5 y=−1 (5,0) x 10 y=0 (−1,0) x 5 x=−1 x=−2 x=1 5. y 10 11. y 10 y=2 (5/2,0) x 10 y=1 (0,0) (2,0) x 10 x=−1 x=−2 x=1 Version: Fall 2007
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7 Rational Functions In this chapte
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Section 7.1 Introducing Rational Fu
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Section 7.6 Complex Fractions 707 5
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Section 7.6 Complex Fractions 709 4
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Section 7.7 Solving Rational Equati
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Section 7.8 Applications of Rationa
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Section 7.9 Index 747 7.9 Index a a
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