Slant asymptote
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- Algebraically Determining the Existence of Slant Asymptotes
Without sketching the graph of the function, determine whether or not each function has a slant asymptote:
- Determining the Equation of a Slant Asymptote Using Long Division
Determine the equations of the slant asymptotes for the following functions using long division.
- Determining the Equation of a Slant Asymptote Using Synthetic Division
Determine the equations of the slant asymptotes for the following functions using long division.
- Graphing Rational Functions Incorporating All 3 Kinds of Asymptotes
Sketch the rational function
f(x)=x+22x2−x−6
by determining:
i) points of discontinuity
ii) vertical asymptotes
iii) horizontal asymptotes
iv) slant asymptote
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Topic Notes
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.
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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