What does it mean when the intervals of a function are increasing or decreasing? For example,w hat does it mean when it says a function is decreasing on the interval $(-\infty, 0)$ or for example or increasing on the interval $(0,-\infty)$?
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$\begingroup$A function $f$ is increasing on an interval $I$ if whenever $x$ and $y$ are points in the interval, if $x$ is larger than $y$, then $f(x)$ is larger than $f(y)$. In other words, $f$ is increasing on an interval $I$ if for all $x, y \in I$ with $x > y$, then $f(x) > f(y)$.
Likewise, a function $f$ is decreasing on an interval $I$ if for all $x, y \in I$ with $x > y$, then $f(x) < f(y)$.
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