Analisis Grafico 3 Ejercicios

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Analisis Grafico 3 Ejercicios

  1. 1. Análisis Gráfico de Funciones (Resultados de Ejercicios)
  2. 2. Resultados de ejercicios para practicar:
  3. 3. Resultados de ejercicios para practicar: Df = R = (−∞; ∞)
  4. 4. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞)
  5. 5. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3
  6. 6. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞)
  7. 7. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  8. 8. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  9. 9. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  10. 10. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) I.C. = (−∞; −1,2) U (1,8; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  11. 11. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) I.C. = (−∞; −1,2) U (1,8; ∞) X1 = −2 Ceros: X2 = 0 I.D. = (−1,2; 1,8) X3 = 3 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  12. 12. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) I.C. = (−∞; −1,2) U (1,8; ∞) X1 = −2 Ceros: X2 = 0 I.D. = (−1,2; 1,8) X3 = 3 f(0) = 0 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3)
  13. 13. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) I.C. = (−∞; −1,2) U (1,8; ∞) X1 = −2 Ceros: X2 = 0 I.D. = (−1,2; 1,8) X3 = 3 f(0) = 0 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3) Máx. Abs. No tiene Mín. Abs. No tiene
  14. 14. Resultados de ejercicios para practicar: Df = R = (−∞; ∞) Máx. Rel. = (−1,2; 1,4) Mín. Rel. = (1,8; −2,7) If = R = (−∞; ∞) I.C. = (−∞; −1,2) U (1,8; ∞) X1 = −2 Ceros: X2 = 0 I.D. = (−1,2; 1,8) X3 = 3 f(0) = 0 C+ = (−2; 0) U (3; ∞) C− = (−∞; −2) U (0; 3) Máx. Abs. No tiene Mín. Abs. No tiene Asíntotas: No tiene
  15. 15. Df = R = (−∞; ∞)
  16. 16. Df = R = (−∞; ∞) If = [−2,5; ∞)
  17. 17. Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3
  18. 18. Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞)
  19. 19. Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  20. 20. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  21. 21. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  22. 22. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) I.C. = (-2,2; 0) U (2,2; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  23. 23. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) I.C. = (-2,2; 0) U (2,2; ∞) X1 = −3 I.D. = (-∞; -2,2) U (0; 2,2) Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  24. 24. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) I.C. = (-2,2; 0) U (2,2; ∞) X1 = −3 I.D. = (-∞; -2,2) U (0; 2,2) Ceros: X2 = 0 X3 = 3 f(0) = 0 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
  25. 25. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) I.C. = (-2,2; 0) U (2,2; ∞) X1 = −3 I.D. = (-∞; -2,2) U (0; 2,2) Ceros: X2 = 0 X3 = 3 f(0) = 0 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3) Máx. Abs. No tiene Mín. Abs. -2,5
  26. 26. Máx. Rel. = (0; 0) Df = R = (−∞; ∞) Mín. Rel. = {(-2,2; -2,5),(2,2; -2,5)} If = [−2,5; ∞) I.C. = (-2,2; 0) U (2,2; ∞) X1 = −3 I.D. = (-∞; -2,2) U (0; 2,2) Ceros: X2 = 0 X3 = 3 f(0) = 0 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3) Máx. Abs. No tiene Mín. Abs. -2,5 Asíntotas: No tiene
  27. 27. Df = R = (−∞; ∞)
  28. 28. Df = R = (−∞; ∞) If = [−0,8; ∞)
  29. 29. Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1
  30. 30. Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞)
  31. 31. Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
  32. 32. Máx. Rel. No tiene Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
  33. 33. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
  34. 34. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) I.C. = (-2,5; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
  35. 35. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) I.C. = (-2,5; ∞) Ceros: X1 = −1 I.D. = (-∞; -2,5) C+ = (-1; ∞) C- = (-∞; -1)
  36. 36. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) I.C. = (-2,5; ∞) Ceros: X1 = −1 I.D. = (-∞; -2,5) C+ = (-1; ∞) f(0) = 3 C- = (-∞; -1)
  37. 37. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) I.C. = (-2,5; ∞) Ceros: X1 = −1 I.D. = (-∞; -2,5) C+ = (-1; ∞) f(0) = 3 C- = (-∞; -1) Máx. Abs. No tiene Mín. Abs.= -0,8
  38. 38. Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) I.C. = (-2,5; ∞) Ceros: X1 = −1 I.D. = (-∞; -2,5) C+ = (-1; ∞) f(0) = 3 C- = (-∞; -1) Máx. Abs. No tiene Mín. Abs.= -0,8 Asíntota Horizontal y = 0
  39. 39. Df = R – { 3 }
  40. 40. Df = R – { 3 } If = R – { 1 }
  41. 41. Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5
  42. 42. Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞)
  43. 43. Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
  44. 44. Máx. Rel. = No tiene Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
  45. 45. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
  46. 46. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } I.C. = No tiene Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
  47. 47. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } I.C. = No tiene Ceros: X1 = 2,5 I.D. = (-∞; 3) U (3; ∞) C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
  48. 48. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } I.C. = No tiene Ceros: X1 = 2,5 I.D. = (-∞; 3) U (3; ∞) C+ = (−∞; 2,5) U (3; ∞) f(0) = 0,8 C− = (2,5; 3)
  49. 49. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } I.C. = No tiene Ceros: X1 = 2,5 I.D. = (-∞; 3) U (3; ∞) C+ = (−∞; 2,5) U (3; ∞) f(0) = 0,8 C− = (2,5; 3) Máx. Abs. No tiene Mín. Abs. No tiene
  50. 50. Máx. Rel. = No tiene Df = R – { 3 } Mín. Rel. = No tiene If = R – { 1 } I.C. = No tiene Ceros: X1 = 2,5 I.D. = (-∞; 3) U (3; ∞) C+ = (−∞; 2,5) U (3; ∞) f(0) = 0,8 C− = (2,5; 3) Máx. Abs. No tiene Asíntota Vertical x = 3 Mín. Abs. No tiene Asíntota Horizontal y = 1
  51. 51. Df = R – {-2; 4}
  52. 52. Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞)
  53. 53. Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene
  54. 54. Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞)
  55. 55. Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  56. 56. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  57. 57. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  58. 58. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) I.C. = (-∞; -2) U (-2; 1) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  59. 59. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) I.C. = (-∞; -2) U (-2; 1) Ceros: No tiene I.D. = (1; 4) U (4; ∞) C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  60. 60. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) I.C. = (-∞; -2) U (-2; 1) Ceros: No tiene I.D. = (1; 4) U (4; ∞) f(0) = -1 C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
  61. 61. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) I.C. = (-∞; -2) U (-2; 1) Ceros: No tiene I.D. = (1; 4) U (4; ∞) f(0) = -1 C+ = (−∞; −2) U (4; ∞) C− = (−2; 4) Máx. Abs. No tiene Mín. Abs. No tiene
  62. 62. Máx. Rel. = (1; -0,9) Df = R – {-2; 4} Mín. Rel. = No tiene If = (-∞; -0,9] U (0; ∞) I.C. = (-∞; -2) U (-2; 1) Ceros: No tiene I.D. = (1; 4) U (4; ∞) f(0) = -1 C+ = (−∞; −2) U (4; ∞) C− = (−2; 4) Máx. Abs. No tiene Mín. Abs. No tiene Asíntotas Verticales x = -2 ∧ x = 4 Asíntota Horizontal y = 0
  63. 63. Df = (0; ∞)
  64. 64. Df = (0; ∞) If = R = (-∞; ∞)
  65. 65. Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1
  66. 66. Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞)
  67. 67. Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
  68. 68. Máx. Rel. = No tiene Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
  69. 69. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
  70. 70. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
  71. 71. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) I.D. = No tiene Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
  72. 72. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) I.D. = No tiene Ceros: X1 = 1 f(0) = No existe C+ = (1; ∞) C- = (0; 1)
  73. 73. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) I.D. = No tiene Ceros: X1 = 1 f(0) = No existe C+ = (1; ∞) C- = (0; 1) Máx. Abs. No tiene Mín. Abs. No tiene
  74. 74. Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) I.D. = No tiene Ceros: X1 = 1 f(0) = No existe C+ = (1; ∞) C- = (0; 1) Máx. Abs. No tiene Mín. Abs. No tiene Asíntota Vertical: x = 0
  75. 75. Df = R = (−∞; ∞)
  76. 76. Df = R = (−∞; ∞) If = [-2,5; 2,5]
  77. 77. Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0
  78. 78. Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞)
  79. 79. Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
  80. 80. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
  81. 81. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
  82. 82. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] I.C. = (-0,4; 0,4) Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
  83. 83. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] I.C. = (-0,4; 0,4) Ceros: X1 = 0 I.D. = (-∞; -0,4) U (0,4; ∞) C+ = (0; ∞) C- = (−∞; 0)
  84. 84. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] I.C. = (-0,4; 0,4) Ceros: X1 = 0 I.D. = (-∞; -0,4) U (0,4; ∞) C+ = (0; ∞) f(0) = 0 C- = (−∞; 0)
  85. 85. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] I.C. = (-0,4; 0,4) Ceros: X1 = 0 I.D. = (-∞; -0,4) U (0,4; ∞) C+ = (0; ∞) f(0) = 0 C- = (−∞; 0) Máx. Abs. = 2,5 Mín. Abs. = -2,5
  86. 86. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) Mín. Rel. = (-0,4; -2,5) If = [-2,5; 2,5] I.C. = (-0,4; 0,4) Ceros: X1 = 0 I.D. = (-∞; -0,4) U (0,4; ∞) C+ = (0; ∞) f(0) = 0 C- = (−∞; 0) Máx. Abs. = 2,5 Mín. Abs. = -2,5 Asíntota Horizontal: y = 0
  87. 87. Fin de la presentación

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