What does it mean by 'monotone' when referring to functions? To clarify, I know what it means when a function is surjective, injective, bijective, and what its inverse is. This is something my module notes covers.

However, I have a question (past exam paper) asking to show that a function is monotone. I have no clue what it means, and there is not a single mention of it in the module notes (provided by the professor, and I don't have access to a recommended textbook either).

Please could someone explain what monotone means?
A real valued function $f$ of a real variable is monotonically increasing if
$$
f(a) \ge f(b) \text{ when } a &gt; b.
$$
"Monotone" might be monotonically increasing or monotonically decreasing. Sometimes you want the inequality to exclude equality. Then you use the adjective "strictly".
A monotonic function is one that preserves some sort of well-defined "order". Some examples are:


a monotonically increasing function $f$, such that $f(x)&lt;f(x+\epsilon)$ for all $\epsilon&gt;0$,
a monotonically decreasing function $f$, such that $f(x)&gt;f(x+\epsilon)$ for all $\epsilon&gt;0$.