First of all, do polynomials have asymptotes, including oblique ones? I know that rational functions have asymptotes, and it seems that most, if not all, of my book's exercises on this lesson contain only rational functions. So do polynomials have asymptotes? and if so, how do I determine them?(adsbygoogle = window.adsbygoogle || []).push({});

for example, let f(x) = 2 - 15x + 9x^{2}- x^{3}

factoring, i get: f(x) = (-1)(x - 2)(x^{2}+ 7x + 1)

as x approaches posititve or negative infinity, f increases/decreases without bound. So I know that f does not have any horizontal asymptotes. And I'm guessing that because f is defined everywhere, f does not have any vertical asymptotes... As for oblique asymptotes, I have no idea how to find them out.

so after all this reasoning, I'm beginning to think that polynomials do not have any asymptotes...but I wouldn't be surprised if I'm totally wrong either! :tongue2:

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# Do polynomials have asymptotes?

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