#[Continuous function][Función continua]#
Let $x = a$ be a point in the domain of the function $f.$ Then $f$ is continuous at $x = a$ if
both of the following are true:
1. $\displaystyle \lim_{x \to a} f(x)$ exists.\t $\qquad$ \t
\\ 2. $\displaystyle \lim_{x \to a} f(x) = f(a)$ \t \t
The function $f$ is said to be
continuous on its domain if it is continuous at every point in its domain. If $f$ is not continuous at a particular point, $a$, in its domain, we say that $f$ is
discontinuous at $x = a$ or that $f$ has a
discontinuity at $x = a$.