Graphing Rational Functions

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Presentation transcript:

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 pages 648–650 Exercises 1. 2. 5. 6. 0 7. 2 8. –2 9. 2 10. x = 2, y = 0 11. x = –1, y = 0 12. x = 1, y = –1 13. x = 0, y = 2 3. 4. 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 14. x = 0; 15. x = 0; 16. x = –1; 17. x = 5; 18. x = –4; 19. x = –4; 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 20. x = 0, y = –5; 21. x = 0, y = 5; 22. x = 0, y = –6; 23. x = –1, y = 4; 24. x = 3, y = –5; 25. x = 1, y = –2; 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 26. line with slope 4, y-int. 1 27. absolute value function with vertex (4, 0) 28. exponential decay 29. line with slope , y-int. 0 30. rational function, with asymptotes x = 0, y = 1 31. radical function; y = x shifted right 4, up 1 32. parabola with axis of symmetry x = 0 33. rational function with asymptotes x = –4, y = –1 34. parabola with axis of symmetry x = – 35. moves graph 1 unit to the left 1 4 36. moves graph 3 units to the right 37. lowers graph 15 units 38. moves graph 12 units left 39. moves the graph up 12 units 40. moves the graph left 3 units 41. moves the graph down 2 units 42. moves the graph 3 units left and 2 units down 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 43. x = 0, y = 0; 44. x = 0, y = 0; 45. x = –4, y = 0; 46. x = 0, y = 1; 47. x = –1, y = 4; 48. x = –1, y = –3; 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 49. x = 1, y = 3; 50. x = –5, y = 1; 51. x = 3, y = –2; 52. Answers may vary. Sample: ƒ(x) = + 3, g(x) = 53. 17.8 lumens; 1.97 lumens 54. a. b. x = 0, y = 0; x = 0, y = 0 c. y is any real number except 0; y > 0. 1 x 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 55. a. d 40 b. 16; 1600; 160,000 c. The signal is extremely strong when you are in the immediate vicinity of a transmitter and it will interfere with the other station. 56. The graph of y = and y = – are both composed of two curves with asymptotes x = 0 and y = 0. The graph of y = – is a reflection of the graph of y = over the y-axis. 57. 58. > – 3 x 3 x 3 x 3 x 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 59. 60. 61. a. x = –3, y = –2 b. y = – 2 62. No; ƒ(x) = is equivalent to g(x) = x + 1 for all values except x = –2. 63. C 64. I 65. A 66. C (x + 2)(x + 1) x + 2 1 x + 3 12-2

Graphing Rational Functions ALGEBRA 1 LESSON 12-2 67. [2] a. The graph of g(x) = + 5 is a translation of ƒ(x) = 5 units up and 1 unit right. b. x = 1 and y = 5 [1] one part answered correctly 68. xy = 21 69. xy = 16 70. xy = 22 71. xy = 21.08 72. 0 73. 1 74. 2 4 x – 1 75. 3(d – 6)(d + 6) 76. 2(m – 12)(m + 5) 77. (t 2 + 3)(t – 1) 4 x 12-2