# Slant asymptote

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##### Intros

###### Lessons

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##### Examples

###### Lessons

**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

$f(x) = \frac{2x^{2} - x - 6}{x + 2}$

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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