Linear Oblique Asymptotes

LOA

For rational functions, a linear oblique asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator

Sometimes, there is no horizontal asymptote, and instead, an asymptote in the form of

There cannot be a horizontal asymptote if there is a LOA and vice versa

Example

1. Determine the linear oblique asymptote of

   Divide by using Polynomial Long Division
   
   

   As ,
   Therefore, the is insignificant, leaving just Big Little Concept

   Therefore the eqn of the LOA is

2. Sketch

   Because the equation is not in the form of , the points have to be tested near asymptotes 🤮

   • No hole
   • VA:
   • Test where the points are near the sides of the asymptotes
   • No HA
   • LOA =
   • determine x-int, y-int

Sketch graph with Big Little Concept in mind