Monotone function

A function $f:I\rightarrow \bf{R}$, where $I$ is a subset of $\bf{R}$ is called monotone if it's ether increasing or decreasing:

• if $x≤x'$ then $f(x)≤f(x')$, or
• if $x≤x'$ then $f(x)≥f(x')$.