Intermediate value property

Definition

A function $f$ is said to satisfy the intermediate value property if, for every $a<b$ in the domain of $f$, and every choice of real number $t$ between $f(a)$ and $f(b)$, there exists $c\in [a,b]$ that is in the domain of $f$ such that $f(c)=t$.

Facts

• Intermediate value theorem: This states that a continuous function on a closed interval satisfies the intermediate value property.
• Derivative of differentiable function on interval satisfies intermediate value property