Show that every polynomial function is continuous. - Vidyadip

Question

Show that every polynomial function is continuous.

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Answer

Recall that a function p is a polynomial function if it is defined by p(x) = a₀ + a₁ x + ... + a_n xⁿ for some natural number n, a_n $\neq$ 0 and a_i ∈ R. Clearly this function is defined for every real number. For a fixed real number c, we have
$\mathop {\lim }\limits_{x \to c} p(x)$= p (c)
By definition, p is continuous at c. Since c is any real number, p is continuous at every real number and hence p is a continuous function.

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