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 $f(a) > f(b)$.