Intermediate Value Property

See Intermediate Value Theorem for an application of this. This is only really needed for a homework problem, where in contrast to the IVT we don't care about continuity. (In fact, this property doesn't imply Continuity, where a counter example would be if the function is monotone)

intermediate value property

A function $f$ has the intermediate value property on an interval $[a, b]$ if for all $x < y \in [a, b]$ and all $L$ between $f (x), f (y)$ , it is always possible to find a point $c \in (x, y)$ where $f (c) = L$ .

The idea is that every continuous function on $[a, b]$ has the Intermediate Value Property, but not the other way around.