Question

How to find the asymptotes of `f(x) =3/(2x-1)` ?

Answer 1

Vertical asymptote: `x=1/2`
Horizontal asymptote: `f(x)=0`

Explanation:

Given
`color(white)("XXX")f(x)=3/(2x-1)`

`f(x)rarr +-oo` as `(2x-1) rarr 0`
`color(white)("XXX")2x-1=0 rarr x=1/2`
giving a vertical asymptote at `x=1/2`

`f(x)=3/(2x-1)`
`rarr 2x-1=3/f(x)`
`rarr x= 3/(2f(x)) +1/2`
`color(white)("XXX")xrarr +-oo` as `f(x)rarr 0`
giving a horizontal asymptote at `f(x)=0`

graph{3/(2x-1) [-12.56, 15.91, -9.15, 5.08]}