# Find all horizontal, vertical, or slant asymptotes 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?

Find all horizontal, vertical, or slant asymptotes
I have been instructed to find all the horizontal, vertical or slant asymptotes of the following function:
$y={x}^{3}-4{x}^{2}$
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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Anna Juarez
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.