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Analisis Grafico 3 Ejercicios
 

Analisis Grafico 3 Ejercicios

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    Analisis Grafico 3 Ejercicios Analisis Grafico 3 Ejercicios Presentation Transcript

    • Análisis Gráfico de Funciones (Resultados de Ejercicios)
    • Resultados de ejercicios para practicar:
    • Resultados de ejercicios para practicar: Df = R = (−∞; ∞)
    • Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞)
    • Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3
    • Resultados de ejercicios para practicar: Df = R = (−∞; ∞) If = R = (−∞; ∞) X1 = −2 Ceros: X2 = 0 X3 = 3 C+ = (−2; 0) U (3; ∞)
    • 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)
    • 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)
    • 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)
    • 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)
    • 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)
    • 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)
    • 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
    • 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
    • Df = R = (−∞; ∞)
    • Df = R = (−∞; ∞) If = [−2,5; ∞)
    • Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3
    • Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞)
    • Df = R = (−∞; ∞) If = [−2,5; ∞) X1 = −3 Ceros: X2 = 0 X3 = 3 C+ = (−∞; −3) U (3; ∞) C− = (−3; 0) U (0; 3)
    • 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)
    • 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)
    • 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)
    • 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)
    • 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. 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
    • 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
    • Df = R = (−∞; ∞)
    • Df = R = (−∞; ∞) If = [−0,8; ∞)
    • Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1
    • Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞)
    • Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
    • Máx. Rel. No tiene Df = R = (−∞; ∞) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
    • Máx. Rel. No tiene Df = R = (−∞; ∞) Mín. Rel. = (-2,5; -0,8) If = [−0,8; ∞) Ceros: X1 = −1 C+ = (-1; ∞) C- = (-∞; -1)
    • 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)
    • 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)
    • 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. 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
    • 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
    • Df = R – { 3 }
    • Df = R – { 3 } If = R – { 1 }
    • Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5
    • Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞)
    • Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
    • Máx. Rel. = No tiene Df = R – { 3 } If = R – { 1 } Ceros: X1 = 2,5 C+ = (−∞; 2,5) U (3; ∞) C− = (2,5; 3)
    • 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)
    • 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)
    • 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)
    • 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. 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
    • 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
    • Df = R – {-2; 4}
    • Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞)
    • Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene
    • Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞)
    • Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
    • Máx. Rel. = (1; -0,9) Df = R – {-2; 4} If = (-∞; -0,9] U (0; ∞) Ceros: No tiene C+ = (−∞; −2) U (4; ∞) C− = (−2; 4)
    • 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)
    • 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)
    • 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)
    • 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. 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
    • 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
    • Df = (0; ∞)
    • Df = (0; ∞) If = R = (-∞; ∞)
    • Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1
    • Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞)
    • Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
    • Máx. Rel. = No tiene Df = (0; ∞) If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
    • Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
    • Máx. Rel. = No tiene Df = (0; ∞) Mín. Rel. = No tiene If = R = (-∞; ∞) I.C. = (0; ∞) Ceros: X1 = 1 C+ = (1; ∞) C- = (0; 1)
    • 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)
    • 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. 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
    • 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
    • Df = R = (−∞; ∞)
    • Df = R = (−∞; ∞) If = [-2,5; 2,5]
    • Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0
    • Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞)
    • Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
    • Máx. Rel. = (0,4; 2,5) Df = R = (−∞; ∞) If = [-2,5; 2,5] Ceros: X1 = 0 C+ = (0; ∞) C- = (−∞; 0)
    • 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)
    • 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)
    • 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)
    • 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. 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
    • 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
    • Fin de la presentación