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# Lesson 5

### Definitions Associated With Graphing Polynomial Functions

Term | Definition |
---|---|

Zero of a Function | The point at which the graph of a polynomial touches or crosses the x-axis, also known as x-intercepts |

Multiplicity | The number of times that a zero's associated factor appears in a polynomial |

Even Multiplicity | The zero TOUCHES the x-axis, but does not cross it. |

Odd Multiplicity | The zero CROSSES the x-axis at this point. |

End Behavior of an Even Degree Polynomial with a Positive Leading Coefficient | The graph rises to the left and rises to the right. |

End Behavior of an Even Degree Polynomial with a Negative Leading Coefficient | The graph falls to the left and falls to the right. |

End Behavior of an Odd Degree Polynomial with a Positive Leading Coefficient | The graph falls to the left and rises to the right. |

End Behavior of an Odd Degree Polynomial with a Negative Leading Coefficient | The graph rises to the left and falls to the right. |

Rational Zero Test | A handy way to obtain a list of possible rational zeros of a function by listing all of the factors of the constant term and dividing by all of the factors of the leading coefficient. |

Extrema | All of the maximum and minimum values of a function |

Relative Maximum | On a small interval, a relative maximum occurs at a point in the interval where the graph is increasing prior to that point and decreasing after that point. |

Relative Minimum | On a small interval, a relative maximum occurs at a point in the interval where the graph is decreasing prior to that point and increasing after that point. |

Absolute Maximum | The highest point that a graph will reach. Please note only functions of even degree will have an absolute maximum. |

Absolute Minimum | The lowest point that a graph will reach. Please note only functions of even degree will have an absolute minimum. |

Strictly Increasing | A function is increasing if the y-values increase as the x-values increase. |

Strictly Decreasing | A function is decreasing if the y-values decrease as the x-values increase. |

Created by:
Kskeener