Horizontal Asymptotes and Slant Asymptotes of Rational Functions

This algebra video tutorial explains how to identify the horizontal asymptotes and slant asymptotes of rational functions by comparing the degree of the numerator with the degree of the denominator of the rational expression. The equation of the slant asymptote can be determine using long division if the degree of the numerator exceeds the degree of the denominator by exactly 1. This algebra video tutorial contains plenty of examples and practice problems.

Algebra - Free Formula Sheets:

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Fundamental Theorem of Algebra:

Rational Expressions - Basic Intro:

Simplifying Rational Expressions:

Multiplying Rational Expressions:

Dividing Rational Expressions:

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Adding & Subtracting Rational Expressions:

Rational Expressions - Unlike Denominators:

Simplifying Complex Rational Expressions:

How To Solve Rational Equations:

Rational Equations - Extraneous Solutions:

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Horizontal and Slant Asymptotes:

Finding Rational Functions Given 2 Points:

Rational Functions - X and Y Intercepts:

Graphing Advanced Rational Functions:

Rational Inequalities:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

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[taiedy]

Sorry, how can there be a slant asymptote if the equation at 5:20 factors cleanly into [x+2] without a remainder? Shouldn't there be a slant asymptote only if it leaves a remainder?

[nejcocepek]

in the first case of slant asymptote the asymptote does not exist since the remainder of long division is zero and if we cancel out the terms we see that we get linear function with equation y = x + 2 with a missing point at x = -3 which lies on the asymptote and that contradicts with the definition of an asymptote