In the study of calculus, understanding how functions behave is crucial. One key aspect of this is identifying when a function is increasing or decreasing.
A function $f(x)$ is said to be increasing on an interval if, for any two points $x_1$ and $x_2$ in that interval where $x_1 < x_2$, we have $f(x_1) < f(x_2)$. Conversely, a function is decreasing on an interval if, for any two points $x_1$ and $x_2$ in that interval where $x_1 < x_2$, we have $f(x_1) > f(x_2)$.
It's important to distinguish between strictly increasing/decreasing and non-strictly increasing/decreasing functions. The definitions above describe strictly increasing/decreasing functions. For non-strict versions, we would use $\leq$ and $\geq$ instead of $<$ and $>$.
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