How do you find all the asymptotes for function f(x) = (3)/(5x)f(x)=35x?

1 Answer
Luca F.
Jun 10, 2015
  • lim_(x->0)(3/(5x))=oo So there is a vertical asymptote in x=0.
  • lim_(x->oo)(3/(5x))=0 So there is a horizontal asymptote in y=0.
  • No oblique asymptotes.

Explanation:

How do we find asymptotes of f(x)?
- Vertical Asymptotes -> lim_(x->a)(f(x))=l where a is a point of discontinuity of f(x). Vertical asymptote in x=a hArr l=oo.
- Horizontal Asymptotes -> lim_(x->+-oo)(f(x))=l. Horizontal asymptote in y=l hArr l!=oo.
- Oblique Asymptotes hArr there aren't horizontal asymptotes.

Let's verify the solutions found in this case:

graph{3/(5x) [-10, 10, -5, 5]}

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