Question

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

Answer 1

• `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]}