Why are all polynomial functions continuous?

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I need a basic understanding with maybe a rule or proof? Grade 12 here

for ex: 3x^5 + 2x^3 -x

find all x-values for which its continious.

In: Mathematics

For a function to be continuous, its derivative must be always defined. The derivative of a polynomial is a polynomial of smaller order. Also, polynomial functions don’t have undefined values (for polynomials with integer exponents).

This might by >12^th Grade, depending on your school system’s treatment of pre-calculus.