analisis grafico 3 ejercicios
DESCRIPTION
analisis grafico ejerciciosTRANSCRIPT
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
C+ = (−2; 0) U (3; ∞)
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
I.C. = (−∞; −1,2) U (1,8; ∞)
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
I.C. = (−∞; −1,2) U (1,8; ∞)
I.D. = (−1,2; 1,8)X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
I.C. = (−∞; −1,2) U (1,8; ∞)
I.D. = (−1,2; 1,8)
f(0) = 0
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
I.C. = (−∞; −1,2) U (1,8; ∞)
I.D. = (−1,2; 1,8)
Máx. Abs. No tiene
Mín. Abs. No tiene
f(0) = 0
X3 = 3
Resultados de ejercicios para practicar:
Df = R = (−∞; ∞)
If = R = (−∞; ∞)
X1 = −2
Ceros: X2 = 0
C+ = (−2; 0) U (3; ∞)
C− = (−∞; −2) U (0; 3)
Máx. Rel. = (−1,2; 1,4)
Mín. Rel. = (1,8; −2,7)
I.C. = (−∞; −1,2) U (1,8; ∞)
I.D. = (−1,2; 1,8)
Máx. Abs. No tiene
Mín. Abs. No tiene Asíntotas: No tiene
f(0) = 0
X3 = 3
Df = R = (−∞; ∞)
Df = R = (−∞; ∞)
If = [−2,5; ∞)
Df = R = (−∞; ∞)
If = [−2,5; ∞)
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}Mín. Rel. =
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}
I.C. = (-2,2; 0) U (2,2; ∞)
Mín. Rel. =
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}
I.C. = (-2,2; 0) U (2,2; ∞)
I.D. = (-∞; -2,2) U (0; 2,2)
Mín. Rel. =
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}
I.C. = (-2,2; 0) U (2,2; ∞)
I.D. = (-∞; -2,2) U (0; 2,2)
Mín. Rel. =
f(0) = 0
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}
I.C. = (-2,2; 0) U (2,2; ∞)
I.D. = (-∞; -2,2) U (0; 2,2)
Máx. Abs. No tiene
Mín. Abs. -2,5
Mín. Rel. =
f(0) = 0
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
If = [−2,5; ∞)
C+ = (−∞; −3) U (3; ∞)
C− = (−3; 0) U (0; 3)
Máx. Rel. = (0; 0)
{(-2,2; -2,5),(2,2; -2,5)}
I.C. = (-2,2; 0) U (2,2; ∞)
I.D. = (-∞; -2,2) U (0; 2,2)
Máx. Abs. No tiene
Mín. Abs. -2,5 Asíntotas: No tiene
Mín. Rel. =
f(0) = 0
X1 = −3
Ceros: X2 = 0
X3 = 3
Df = R = (−∞; ∞)
Df = R = (−∞; ∞)
If = [−0,8; ∞)
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)Mín. Rel. =
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)
I.C. = (-2,5; ∞)
Mín. Rel. =
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)
I.C. = (-2,5; ∞)
I.D. = (-∞; -2,5)
Mín. Rel. =
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)
I.C. = (-2,5; ∞)
I.D. = (-∞; -2,5)
Mín. Rel. =
f(0) = 3
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)
I.C. = (-2,5; ∞)
I.D. = (-∞; -2,5)
Máx. Abs. No tiene
Mín. Abs.= -0,8
Mín. Rel. =
f(0) = 3
Df = R = (−∞; ∞)
If = [−0,8; ∞)
X1 = −1Ceros:
C+ = (-1; ∞)
C- = (-∞; -1)
Máx. Rel. No tiene
(-2,5; -0,8)
I.C. = (-2,5; ∞)
I.D. = (-∞; -2,5)
Máx. Abs. No tiene
Mín. Abs.= -0,8 Asíntota Horizontal y = 0
Mín. Rel. =
f(0) = 3
Df = R – { 3 }
Df = R – { 3 }
If = R – { 1 }
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tiene
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tieneMín. Rel. =
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tiene
I.C. = No tiene
Mín. Rel. =
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tiene
I.C. = No tiene
I.D. = (-∞; 3) U (3; ∞)
Mín. Rel. =
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tiene
I.C. = No tiene
I.D. = (-∞; 3) U (3; ∞)
Mín. Rel. =
f(0) = 0,8
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tiene
I.C. = No tiene
I.D. = (-∞; 3) U (3; ∞)
Máx. Abs. No tiene
Mín. Abs. No tiene
Mín. Rel. =
f(0) = 0,8
Df = R – { 3 }
If = R – { 1 }
X1 = 2,5Ceros:
C+ = (−∞; 2,5) U (3; ∞)
C− = (2,5; 3)
Máx. Rel. = No tieneNo tiene
I.C. = No tiene
I.D. = (-∞; 3) U (3; ∞)
Máx. Abs. No tiene
Mín. Abs. No tiene
Mín. Rel. =
f(0) = 0,8
Asíntota Vertical x = 3
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)
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)
Mín. Rel. = No tiene
Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)
Máx. Rel. = (1; -0,9)
I.C. = (-∞; -2) U (-2; 1)
Mín. Rel. = No tiene
Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)
Máx. Rel. = (1; -0,9)
I.C. = (-∞; -2) U (-2; 1)
I.D. = (1; 4) U (4; ∞)
Mín. Rel. = No tiene
Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)
Máx. Rel. = (1; -0,9)
I.C. = (-∞; -2) U (-2; 1)
I.D. = (1; 4) U (4; ∞)
Mín. Rel. = No tiene
f(0) = -1
Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)
Máx. Rel. = (1; -0,9)
I.C. = (-∞; -2) U (-2; 1)
I.D. = (1; 4) U (4; ∞)
Máx. Abs. No tiene
Mín. Abs. No tiene
Mín. Rel. = No tiene
f(0) = -1
Df = R – {-2; 4}
If = (-∞; -0,9] U (0; ∞)
Ceros: No tiene
C+ = (−∞; −2) U (4; ∞)
C− = (−2; 4)
Máx. Rel. = (1; -0,9)
I.C. = (-∞; -2) U (-2; 1)
I.D. = (1; 4) U (4; ∞)
Máx. Abs. No tiene
Mín. Abs. No tiene
Mín. Rel. = No tiene
f(0) = -1
Asíntotas Verticales x = -2 ∧ x = 4
Asíntota Horizontal y = 0
Df = (0; ∞)
Df = (0; ∞)
If = R = (-∞; ∞)
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tieneMín. Rel. = No tiene
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
I.C. = (0; ∞)
Mín. Rel. = No tiene
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
I.C. = (0; ∞)I.D. = No tiene
Mín. Rel. = No tiene
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
I.C. = (0; ∞)I.D. = No tiene
Mín. Rel. = No tiene
f(0) = No existe
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
I.C. = (0; ∞)I.D. = No tiene
Máx. Abs. No tiene
Mín. Abs. No tiene
Mín. Rel. = No tiene
f(0) = No existe
Df = (0; ∞)
If = R = (-∞; ∞)
X1 = 1Ceros:
C+ = (1; ∞)
C- = (0; 1)
Máx. Rel. = No tiene
I.C. = (0; ∞)I.D. = No tiene
Máx. Abs. No tiene
Mín. Abs. No tiene Asíntota Vertical: x = 0
Mín. Rel. = No tiene
f(0) = No existe
Df = R = (−∞; ∞)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
Mín. Rel. = (-0,4; -2,5)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
I.C. = (-0,4; 0,4)
Mín. Rel. = (-0,4; -2,5)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
I.C. = (-0,4; 0,4)
I.D. = (-∞; -0,4) U (0,4; ∞)
Mín. Rel. = (-0,4; -2,5)
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
I.C. = (-0,4; 0,4)
I.D. = (-∞; -0,4) U (0,4; ∞)
Mín. Rel. = (-0,4; -2,5)
f(0) = 0
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
I.C. = (-0,4; 0,4)
I.D. = (-∞; -0,4) U (0,4; ∞)
Máx. Abs. = 2,5
Mín. Abs. = -2,5
Mín. Rel. = (-0,4; -2,5)
f(0) = 0
Df = R = (−∞; ∞)
If = [-2,5; 2,5]
X1 = 0Ceros:
C+ = (0; ∞)
C- = (−∞; 0)
Máx. Rel. = (0,4; 2,5)
I.C. = (-0,4; 0,4)
I.D. = (-∞; -0,4) U (0,4; ∞)
Máx. Abs. = 2,5
Mín. Abs. = -2,5 Asíntota Horizontal: y = 0
Mín. Rel. = (-0,4; -2,5)
f(0) = 0
Fin de la presentación