Definition: We say that a  $f$  is (montonically)  increasing for a set  D, if whenever $a < b $ for $a$ and $ b \in D$ , $f(a) < f(b)$.
We say that a  $f$  is (montonically)  decreasing if whenever $a < b $ for $a$ and $ b \in D$, $f(a) > f(b)$.

	Graph	Mapping Diagram
Increasing: If $a < b $ then $f(a) < f(b)$.
Decreasing: If $a < b $ then $f(a) > f(b)$.