Intermediate value property

A real function is said to have the intermediate value property on an interval $[a, b]$ if, for each value $v$ between $f(a)$ and $f(b)$, there is some $c \in (a, b)$ such that $f(c) = v$. Thus, a function with the intermediate value property takes all intermediate values between any two points.

The simplest, and most important, examples of functions with this property are the continuous functions.

This article is a stub. Help us out by expanding it.