__• Definition of "continuity" in everyday language__

A function is

**continuous**if it has no

*holes, asymptotes, or breaks*. A

**continuous**graph can be drawn without removing your pen from the paper.

__• Definition of "__

**continuity**" in CalculusA function $f$ is

**continuous at a number a**, if: $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)$

__• Polynomials are always continuous everywhere.__Rational functions are continuous wherever the functions are defined; in other words, avoiding holes and asymptotes, rational functions are continuous everywhere. A function f is continuous at a number a, if and only if:

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

In simple words, the graph of a continuous function has no break in it and can be drawn without lifting your pen from the paper.