Increasing vs decreasing functions

Question

Some of the literatures use increasing and nondecreasing interchangeably. What can we say about functions that are neither increasing nor decreasing?

Answer 1

Easier to understand explanation:

Any graph where $y$ is affected by $x$ will either increase or decrease at various points, sometimes multiple times. E.g. $y=ax+b$ is strictly increasing if $a>0$ and strictly decreasing if $a<0$, whilst any curves will have points at which the curve increases or decreases. So the only way for a curve to be neither increasing nor decreasing is if $x$ doesn't affect it, or rather, where $y=c$ where $c$ is a constant.

Better explanation:

If a curve $y=f(x)$ is neither increasing nor decreasing, then $f'(x)\equiv0$ $ \forall x$. Integrating then tells us $f(x)\equiv\int(0)\equiv0+C=C$ (where $C$ is the constant of integration)