Monotonically increasing

In calculus and analysis

A function is termed monotonically increasing (also increasing or non-decreasing) if for all ${\displaystyle x}$ and ${\displaystyle y}$ such that ${\displaystyle x\leq y}$ one has ${\displaystyle f\!\left(x\right)\leq f\!\left(y\right)}$, so ${\displaystyle f}$ preserves the order (see Figure 1). Likewise, a function is called monotonically decreasing (also decreasing or non-increasing) if, whenever ${\displaystyle x\leq y}$, then ${\displaystyle f\!\left(x\right)\geq f\!\left(y\right)}$, so it reverses the order (see Figure 2).