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

1 Answer
Jun 10, 2015

Answer:

  • #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]}