analisis grafico 3 ejercicios

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