# Math 22 Asymptotes

Revision as of 08:34, 23 October 2020 by Tphan046 (talk | contribs) (→Horizontal Asymptotes of Rational Functions)

## Vertical Asymptotes and Infinite Limits

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If approaches infinity (or negative infinity) as approaches from the right or from the left, then the line is a vertical asmptote of the graph of

**Example**: Find the a vertical Asymptotes as below:

**1)**

Solution: |
---|

Notice |

Let the denominator equals to zero, ie: , hence or |

Therefore, has vertical asymptotes at and |

**2)**

Solution: |
---|

Notice |

Let the denominator equals to zero, ie: , hence |

Therefore, has vertical asymptote at |

## Definition of Horizontal Asymptote

If is a function and and are real numbers, then the statements and denote limits at infinity. The line and are horizontal asymptotes of the graph of

## Horizontal Asymptotes of Rational Functions

```
Let be a rational function.
1. If the degree of the numerator is less than the degree of the denominator,
then is a horizontal asymptote of the graph of (to the left and to the right).
2. If the degree of the numerator is equal to the degree of the denominator,
then is a horizontal asymptote of the graph of (to the left and to the right),
where and are the leading coefficients of and , respectively.
3. If the degree of the numerator is greater than the degree of the denominator,
then the graph of has no horizontal asymptote.
```

**This page were made by Tri Phan**