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# Rational Functions

### What to do

What is | Answer |
---|---|

The rule for horizontal asymptotes if the degree of p is smaller than the degree of q... | The horizontal asymptote is y = 0 which is the x-axis. Make a dashed line across the x-axis. |

The rule for horizontal asymptotes if the degree of p is equal to the degree of q.... | Make a fraction out of the leading coefficients of p and q. Write an equation y = fraction. Graph as a dashed horizontal line. |

The first step in finding the domain of a Rational Expression... | ... SET THE DENOMINATOR NOT EQUAL TO ZERO. Then, find any Greatest Common Factor (GCF). Then, factor if possible. Finally, set each piece not equal to zero and solve. Domain is always all real numbers except whatever exclusions you found. |

The first step in finding the x-intercept of a Rational Expression... | ...set the NUMERATOR equal to zero. Find any GCF. Factor, if possible. Set each term equal to zero. Solve for the variable. |

The first step in finding the vertical asymptote of a Rational expression... | ...Set the denominator of the expression EQUAL (yes, equal) to zero. Find any GCF of the denominator. Then, factor the denominator. Set each term equal to zero, then solve for the variable. Draw a dashed line on the graph for each vertical asymptote. |

The first step in simplifying a Rational Expression... | ...find the GCF of the numerator. Then, factor the numerator. Next, find the GCF of the denominator. Then, factor the denominator. When everything is completely factored, you can cross like terms in the numerator and denominator out. |

The first step in finding the excluded value of a Rational Expression.... | The first step in finding the excluded value of a rational expression is to SET THE DENOMINATOR NOT EQUAL TO ZERO. Then, find any Greatest Common Factor (GCF). Then, factor if possible. Finally, set each piece not equal to zero and solve. |

The rule for horizontal asymptotes if the degree of p is larger than the degree of q... | There is no horiztal asymptote. However, if the degree of p is only one larger than the degree of q there is a slant asymptote which can be found by doing synthetic or long division to find an equation in slope-intercept form y = mx + b |

...the first step in solving a rational EQUATION | Find the GCF and Factor each denominator. Then, use that information to find the Least Common Denominator (LCD). Multiply each term by the LCD. |

Created by:
sassymath