Question

How do I find the asymptotes of `y=1/((x-1)(x-3))`?

Answer 1

Horizontal is when `limxto+-oo1/((x-3)(x-1))=0`

and vertical is when x is 1 or 3

Explanation:

The horizontal assymptotes are the assymptotes as x approaches infinity or negative infinity `limxtooo` or `limxto-oo`

`limxtooo 1/(x^2-4x+3)`

Divide top and bottom by the highest power in the denominator
`limxtooo (1/x^2)/(1-4/x+3/x^2)`

`0/(1-0-0)=0/1=0` so this is your horizontal assymptote negative infinty gives us the same result

For the vertical asymptote we are looking for when the denominator is equal to zero

`(x-1)(x-3)=0` so you have a vertical asymptote when

`x=3 or 1`