Slant asymptote  Rational Functions
Slant asymptote
When the polynomial in the numerator is exactly one degree higher than the polynomial in the denominator, there is a slant asymptote in the rational function. To determine the slant asymptote, we need to perform long division.
Basic Concepts
 Polynomial long division
 Polynomial synthetic division
Related Concepts
 Curve sketching
Lessons
Notes:
For a simplified rational function, when the numerator is exactly one degree higher than the denominator, the rational function has a slant asymptote. To determine the equation of a slant asymptote, we perform long division.

1.
Algebraically Determining the Existence of Slant Asymptotes
Without sketching the graph of the function, determine whether or not each function has a slant asymptote:

2.
Determining the Equation of a Slant Asymptote Using Long Division
Determine the equations of the slant asymptotes for the following functions using long division.

3.
Determining the Equation of a Slant Asymptote Using Synthetic Division
Determine the equations of the slant asymptotes for the following functions using long division.