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.
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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:
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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.
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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.
