A function in which changes, however small, to any x-value result in small changes to the corresponding y-value, without sudden jumps. Technically, a function is continuous at the point c if it meets the following condition: for any positive number ε, however small, there exists a positive number δ such that for all x within the distance δ from c, the value of f(x) will be within the distance ε from f(c). Polynomials, exponential functions, and trigonometric functions are examples of continuous functions.

Did you mean discontinuous?