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

1 Answer
Jan 26, 2016

Answer:

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