analisis grafico ejercicios

1. Análisis Gráfico
de Funciones
(Resultados de Ejercicios)

2. Resultados de ejercicios para practicar:

3. Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)

4. Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)

5. Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
X3 = 3

6. Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
X3 = 3
C+ = (−2; 0) U (3; ∞)

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. 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. 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. 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. 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. 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. 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. 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

16. Df = R = (−∞; ∞)

17. Df = R = (−∞; ∞)
If = [−2,5; ∞)

18. Df = R = (−∞; ∞)
If = [−2,5; ∞)
X1 = −3
Ceros: X2 = 0
X3 = 3

19. Df = R = (−∞; ∞)
If = [−2,5; ∞)
X1 = −3
Ceros: X2 = 0
X3 = 3
C+ = (−∞; −3) U (3; ∞)

20. Df = R = (−∞; ∞)
If = [−2,5; ∞)
X1 = −3
Ceros: X2 = 0
X3 = 3
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)

21. 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)

22. 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)

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
Ceros: X2 = 0
X3 = 3
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)

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
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)

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)

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

27. 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

29. Df = R = (−∞; ∞)

30. Df = R = (−∞; ∞)
If = [−0,8; ∞)

31. Df = R = (−∞; ∞)
If = [−0,8; ∞)
Ceros: X1 = −1

32. Df = R = (−∞; ∞)
If = [−0,8; ∞)
Ceros: X1 = −1
C+ = (-1; ∞)

33. Df = R = (−∞; ∞)
If = [−0,8; ∞)
Ceros: X1 = −1
C+ = (-1; ∞)
C- = (-∞; -1)

34. Máx. Rel. No tiene Df = R = (−∞; ∞)
If = [−0,8; ∞)
Ceros: X1 = −1
C+ = (-1; ∞)
C- = (-∞; -1)

35. Máx. Rel. No tiene Df = R = (−∞; ∞)
Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞)
Ceros: X1 = −1
C+ = (-1; ∞)
C- = (-∞; -1)

36. 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)

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; ∞)
C- = (-∞; -1)

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)

39. 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

40. 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

42. Df = R – { 3 }

43. Df = R – { 3 }
If = R – { 1 }

44. Df = R – { 3 }
If = R – { 1 }
Ceros: X1 = 2,5

45. Df = R – { 3 }
If = R – { 1 }
Ceros: X1 = 2,5
C+ = (−∞; 2,5) U (3; ∞)

46. Df = R – { 3 }
If = R – { 1 }
Ceros: X1 = 2,5
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)

47. Máx. Rel. = No tiene Df = R – { 3 }
If = R – { 1 }
Ceros: X1 = 2,5
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)

48. 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)

49. 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)

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; ∞)
C− = (2,5; 3)

51. 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)

52. 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

53. 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

55. Df = R – {-2; 4}

56. Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)

57. Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene

58. Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)

59. Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)

60. Máx. Rel. = (1; -0,9) Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)

61. 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)

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
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)

63. 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)

64. 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)

65. 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

66. 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

68. Df = (0; ∞)

69. Df = (0; ∞)
If = R = (-∞; ∞)

70. Df = (0; ∞)
If = R = (-∞; ∞)
Ceros: X1 = 1

71. Df = (0; ∞)
If = R = (-∞; ∞)
Ceros: X1 = 1
C+ = (1; ∞)

72. Df = (0; ∞)
If = R = (-∞; ∞)
Ceros: X1 = 1
C+ = (1; ∞)
C- = (0; 1)

73. Máx. Rel. = No tiene Df = (0; ∞)
If = R = (-∞; ∞)
Ceros: X1 = 1
C+ = (1; ∞)
C- = (0; 1)

74. Máx. Rel. = No tiene Df = (0; ∞)
Mín. Rel. = No tiene
If = R = (-∞; ∞)
Ceros: X1 = 1
C+ = (1; ∞)
C- = (0; 1)

75. Máx. Rel. = No tiene Df = (0; ∞)
Mín. Rel. = No tiene
If = R = (-∞; ∞)
I.C. = (0; ∞)
Ceros: X1 = 1
C+ = (1; ∞)
C- = (0; 1)

76. 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)

77. 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)

78. 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

79. 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

81. Df = R = (−∞; ∞)

82. Df = R = (−∞; ∞)
If = [-2,5; 2,5]

83. Df = R = (−∞; ∞)
If = [-2,5; 2,5]
Ceros: X1 = 0

84. Df = R = (−∞; ∞)
If = [-2,5; 2,5]
Ceros: X1 = 0
C+ = (0; ∞)

85. Df = R = (−∞; ∞)
If = [-2,5; 2,5]
Ceros: X1 = 0
C+ = (0; ∞)
C- = (−∞; 0)

86. Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞)
If = [-2,5; 2,5]
Ceros: X1 = 0
C+ = (0; ∞)
C- = (−∞; 0)

87. 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)

88. 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)

89. 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)

90. 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)

91. 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

92. 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

93. Fin de la presentación