Question

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

Answer 1

Domain is `x!=3`,
Vertical Asymptote is `x=3`
Horizontal Asymptote `y=0`
Slant asymptote none.

Explanation:

To find the domain and vertical asymptote, the denominator is set to be equal to zero
Given `R(x)=2/(x−3)`
Set `x-3=0`

Solving we obtain `x=3`
This gives us the domain and vertical asypmtote.

Since degree of numerator is less than that of the denominator, hence x axis, i.e., `y=0` is horizontal asymptote.

No slant asymptote as degree of numerator is not exactly one more than that of the denominator