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?

Adrien Jordan 2022-09-22 Answered
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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Answers (1)

Anna Juarez
Answered 2022-09-23 Author has 5 answers
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 x 2 + 3 x + 2 x 2 is x+5 because
x 2 + 3 x + 2 x 2 = x + 5 + 12 x 2
and clearly x+5 is the polynomial portion of x 2 + 3 x + 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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