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  1. Discutiendo "Continuidad" gráficamente
    La gráfica de una función ff es mostrada abajo:
    1. Determina los valores en los cuales ff es discontinua
    2. Explica y clasifica cada discontinuidad
      Graph of a function and continuity
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Topic Notes
• Definición de continuidad en lenguaje común:
Una función es continua si no tiene agujeros o asíntotas, así que puede dibujarse sin levantar el lápiz o pluma del papel.

• Definición de continuidad en lenguaje matemático (Cálculo):
Una función ff es continua en un punto a si: limxaf(x)=limxa+f(x)=f(a)\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)

• Los polinomios son siempre continuos: Las funciones racionales son continuas siempre y cuando estén definidas en su dominio; es decir, las funciones racionales son continuas en todos sus puntos excepto cuando su denominador es igual a cero.

En conclusión, una función ff es continua en un punto a si y sólo si:

limxaf(x)=limxa+f(x)=f(a)\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)

graph of a continuous function (a)