Why polynomial functions are continuous

With induction. We will use induction on the degree of a polynomial. The proof is now complete by principle of mathematical induction and every polynomial with real coefficients is continuous everywhere. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 7 years, 7 months ago. Active 3 years, 1 month ago.

Viewed 11k times. If it is an arbitrary real number, your proof is complete. Add a comment. Active Oldest Votes. Hence we can conclude that f1 x Hence all polynomials are continuous. Paramanand Singh Paramanand Singh 77k 12 12 gold badges silver badges bronze badges. There are lots of variations on a theme when it comes to the verbiage used in talking about continuous functions.

For example:. Notice that functions can be discontinuous in a variety of ways all but one of the small pictures above were discontinuous at some point. One can think of functions with removable discontinuities as being ones whose continuity is easily "repairable", in a certain sense.

As can be seen above, removable discontinuities present themselves graphically as " holes " in functions. Graphically, non-removable discontinuities present themselves in a variety of ways, two of which we give names to:.