What does a polynomial function's increasing and decreasing interval mean?

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Now I know that smarter and more interesting question were asked over here, but bear with me. When someone says,"the increasing interval of this polynomial function is (-infinity, 4)," when does it ACTUALLY start to increase? More clearly, at which point in -infinity (if that makes sense) does this function increase?

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1 Answer

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Let us assume that a function $f(x)$ monotonically increases in the range $(-\infty,4)$. This also implies that $f'(x)>0$ for all real values $x\in (-\infty,4)$. You may also choose to think that as you go in the $-x$ direction from $4$, the function always decreases.

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