Asymptotes are like the wind. We can’t see them, yet we can see their effects. There are three types: vertical, horizontal, and slant. On this page, you will find definitions for each type and examples of how to find them. You will also find links to practices problems and quizzes.
Vertical Asymptotes
Vertical asymptotes occur when the denominator (the bottom part of the fraction) equals zero. So just set the denominator equal to zero and solve for x.
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Horizontal Asymptotes
These occur if the largest exponent in the numerator is the same size or less than the largest exponent in the denominator.
Situation 1: The largest exponent in the numerator is the same size as the largest exponent in the denominator.
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Situation 2: The largest exponent in the numerator is less than the largest exponent in the denominator.
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Slant Asymptotes
These occur when the largest exponent in the numerator is greater than the largest exponent in the denominator. In these situations, you have to divide the numerator but the denominator using long division.
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Asymptotes of Tangent Graphs
[ |1/b (π/2)| + Phase Shift] + π/b n
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Practice Problems & Quiz
Click here to take a quiz on vertical and horizontal asymptotes.
Click here to find practice problems with all three types.
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More Math Resources
To see all of our math resources, please click here.
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