Question

How do you find vertical, horizontal and oblique asymptotes for `f(x) = (3)/(5x)`?

Answer 1

vertical asymptote x = 0
horizontal asymptote y = 0

Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation set the denominator equal to zero.

solve 5x = 0 → x = 0 is the asymptote

Horizontal asymptotes occur as

`lim_(xto+-oo),f(x)toc" (a constant)"`

divide numerator/denominator by x

`(3/x)/((5x)/x)=(3/x)/5`

as `xto+-oo,f(x)to0/5`

`rArry=0" is the asymptote"`

Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 0, denominator-degree 1 )Hence there are no oblique asymptotes.
graph{3/(5x) [-10, 10, -5, 5]}