Limits Overview
Limit Notation (Left-Hand, Right-Hand, Overall)
Finding Limits Using a Graph
Finding a Limit Using Equations
Continuity

Option 10: Horizontal Asymptotes (Limits whose x-value is heading towards infinity)

Definition: Horizontal Asymptotes

The horizontal asymptote of an equation is the long-term behavior of an equation. So, for very, very, very large values of x (i.e. ± ) , what y value does it look like your equation would head towards.

You find horizontal asymptotes by taking the limit of an equation as x approaches + , and as x approaches .

lim x f ( x ) = Horizontal Asymptote and   lim x f ( x ) = Horizontal Asymptote

Note:

          The answer to a horizontal asymptote question is always the y value that the equation is heading towards.

          You can have at most 2 horizontal asymptotes. One heading towards + and one heading towards , and they are not always the same value.

          Your equation is allowed to cross the horizontal asymptote.

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