395 3.5 Rational Functions: Graphs, Applications, and Models I 29. ƒ1x2 = x + 7 x + 1 30. ƒ1x2 = x + 10 x + 2 31. ƒ1x2 = 1 x + 4 32. ƒ1x2 = -3 x2 33. ƒ1x2 = x2 - 16 x + 4 34. ƒ1x2 = 4x + 3 x - 7 35. ƒ1x2 = x2 + 3x + 4 x - 5 36. ƒ1x2 = x + 3 x - 6 Concept Check Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. II A. The x-intercept is 1-3, 02. B. The y-intercept is 10, 52. C. The horizontal asymptote is y = 4. D. The vertical asymptote is x = -1. E. There is a hole in its graph at 1-4, -82. F. The graph has an oblique asymptote. G. The x-axis is its horizontal asymptote, and the y-axis is not its vertical asymptote. H. The x-axis is its horizontal asymptote, and the y-axis is its vertical asymptote. Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. 37. ƒ1x2 = 3 x - 5 38. ƒ1x2 = -6 x + 9 39. ƒ1x2 = 4 - 3x 2x + 1 40. ƒ1x2 = 2x + 6 x - 4 41. ƒ1x2 = x2 - 1 x + 3 42. ƒ1x2 = x2 + 4 x - 1 43. ƒ1x2 = x2 - 2x - 3 2x2 - x - 10 44. ƒ1x2 = 3x2 - 6x - 24 5x2 - 26x + 5 45. ƒ1x2 = x2 + 1 x2 + 9 46. ƒ1x2 = 4x2 + 25 x2 + 9 Concept Check Work each problem. 47. Let ƒ be the function whose graph is obtained by translating the graph of y = 1 x to the right 3 units and up 2 units. (a) Write an equation for ƒ1x2 as a quotient of two polynomials. (b) Determine the zero(s) of ƒ. (c) Identify the asymptotes of the graph of ƒ1x2. 48. Repeat Exercise 47 if ƒ is the function whose graph is obtained by translating the graph of y = - 1 x2 to the left 3 units and up 1 unit. 49. After the numerator is divided by the denominator, ƒ1x2 = x5 + x4 + x2 + 1 x4 + 1 becomes ƒ1x2 = x + 1 + x2 - x x4 + 1 . (a) What is the oblique asymptote of the graph of the function? (b) Where does the graph of the function intersect its asymptote? (c) As x S∞, does the graph of the function approach its asymptote from above or below?
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