__• 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 Calculus
A 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.