example of increasing/decreasing/monotone function

The function $f(x)=e^x$ is strictly increasing and hence strictly monotone. Similarly $g(x)=e^{-x}$ is strictly decreasing and hence strictly monotone. Consider the function $h:[1,10]\mapsto [1,5]$ where $h(x)=\sqrt{x-4\sqrt{x-1}+3}+\sqrt{x-6\sqrt{x-1}+8}$. It is not strictly monotone since it is constant on an interval, however it is decreasing and hence monotone.