Show that every polynomial function is continuous.

$A$ function $p$ is defined as a polynomial function if it is of the form $p(x) = a_{0} + a_{1}x + \ldots + a_{n}x^{n}$,where $n$ is a natural number,$a_{n} \neq 0$,and $a_{i} \in \mathbb{R}$.
This function is defined for all real numbers $x \in \mathbb{R}$.
For any arbitrary real number $c$,the limit of the function as $x$ approaches $c$ is given by:
$\lim_{x \to c} p(x) = \lim_{x \to c} (a_{0} + a_{1}x + \ldots + a_{n}x^{n})$
Using the properties of limits,this becomes:
$\lim_{x \to c} p(x) = a_{0} + a_{1}c + \ldots + a_{n}c^{n} = p(c)$
Since $\lim_{x \to c} p(x) = p(c)$ for any real number $c$,the function $p(x)$ is continuous at every point in its domain.
Therefore,every polynomial function is continuous.