Flashcards: Asymptotic behavior in terms of limits involving infinity

Find all vertical asymptotes and horizontal asymptotes of the function, 

 

\displaystyle f(x) = \frac{1-2x^3}{x^3-4x^2+4x}

Horizontal Aysmptotes 

\displaystyle y = 3

 

Vertical Asymptotes 

\displaystyle x =0

\displaystyle x = -1



Horizontal Aysmptotes 

None

 

Vertical Asymptotes 

\displaystyle x =0

\displaystyle x = 2

The horizontal asymptote is, 

\displaystyle y = 2

The vertical asymptotes are, 

\displaystyle x = 2

Horizontal Aysmptotes 

\displaystyle y = 3

 

Vertical Asymptotes 

\displaystyle x =0

 

The horizontal asymptote is, 

\displaystyle y = -2

The vertical asymptotes are, 

\displaystyle x =0

\displaystyle x = 2

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