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Unidad 3: Desigualdades - Prueba rápida

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Unidad 3: Desigualdades - Prueba rápida

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About this activity

Evaluación de conceptos y problemas

Created by

Ana Judith Renderos de Amaya
Ana Judith Renderos de Amaya
El Salvador

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Unidad 3: Desigualdades - Prueba rápida
 

Unidad 3: Desigualdades - Prueba rápidaOnline version

Evaluación de conceptos y problemas

by Ana Judith Renderos de Amaya
1

1) Regla de desigualdades: si a < b y sumas c a ambos lados, la desigualdad se mantiene. ¿Qué forma correcta se obtiene?

2

2) Desigualdad lineal básica: si a > 0, la solución de ax ≥ c es

3

3) Si f(x) es una parábola que abre hacia arriba y f(x1)=f(x2)=0, la desigualdad f(x) ≥ 0 se cumple en

4

4) Desigualdad triangular: |a + b| ≤ |a| + |b| es

5

5) Dominio y rango de f(x)=2x^2 (a>0) es

6

6) Resolver: (x+2)(x−3) ≥ 0. ¿Qué intervalo describe la solución?

7

7) Resolver: 3x − 5 < 2x + 7. ¿Cuál es la solución?

8

8) Resolver: x^2 − 5x + 6 ≤ 0. ¿Qué intervalo es el adecuado?

9

9) Resolver: (x+1)/(x−2) > 0. ¿Cuál es la solución?

10

10) Desigualdad cuadrática: x^2 − 4x − 5 ≥ 0. ¿Qué intervalo describe la solución?

Explicación

La suma de igual cantidad a ambos lados no invierte la relación.

Para coeficiente positivo, divides ambos lados por a sin cambiar el sentido.

Para una parábola que cruza el eje en x1 y x2, es ≥0 fuera del intervalo entre raíces.

Es una propiedad fundamental válida para cualquier par de números reales.

Parábola que abre hacia arriba: dominio real, mínimo en 0.

Producto no negativo cuando ambos factores tienen el mismo signo.

Restas 2x y sumas 5: x < 12.

Factoriza (x-2)(x-3) ≤ 0, raíces en 2 y 3.

cociente positivo fuera de la discontinuidad en 2.

Raíces en 1 y 5; exterior al intervalo.

 
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