A function $g(X)$ is said to be monotonic if it consistently increases or decreases throughout its domain, without reversing direction. **Monotonic increase:** A function is monotonically increasing if, whenever the input $x$ increases to $x^\prime$, the output does not decrease. $ \text{mon. increase} = \begin{cases} x \ge x' \to g(x) \ge g(x') \\ x \leq x' \to g(x) \leq g(x') \end{cases} $ **Monotonic decrease:** A function is monotonically decreasing if, whenever the input $x$ increases to $x^\prime$, the output does not increase. $ \text{mon. decrease} = \begin{cases} x \ge x' \to g(x) \leq g(x') \\ x \leq x' \to g(x) \ge g(x') \end{cases} $ A function is *strictly monotone* if it additionally does not exhibit any plateau. Thus the inequalities $\{\le, \ge\}$ turn into strict inequalities $\{<,>\}$.