I have been instructed to find all the horizontal, vertical or slant asymptotes of the following function:
$$y = x^3-4x^2$$
I know there are no horizontal or vertical asymptotes, but I'm having a hard time understanding slant asymptotes. How do I figure out if there are any of those?
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$\begingroup$The slant asymptote of a function (if it exists) is the part of your function with a polynomial of degree one. For example, the slant asymptote of $\frac{x^2+3x+2}{x-2}$ is $x+5$ because $$\frac{x^2+3x+2}{x-2} = x+5+ \frac{12}{x-2}$$ and clearly $x+5$ is the polynomial portion of $\frac{x^2+3x+2}{x-2}$ with degree one. Your function has no polynomial portion of degree one, so there is no slant asymptote.
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