3.5 - rational functions and their rational functions and their graphs date: 10/25 rational...

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  • 3.5RationalFunctionsandTheirGraphs.notebook

    1

    October25,2016

    3.5:RationalFunctionsandTheirGraphs Date:10/25

    RationalFunctionsarequotientsofpolynomialfunctions.Thismeansthatarationalfunctioncanbeexpressedas:

    Wherepandqarepolynomialfunctionsand

    Thedomainofarationalfunctionisthesetofallrealnumbersexceptthexvaluesthatmakethedenominatorzero.

  • 3.5RationalFunctionsandTheirGraphs.notebook

    2

    October25,2016

    Ex1:Findthedomainofeachrationalfunction.(Useintervalnotation)

    a) b) c)

  • 3.5RationalFunctionsandTheirGraphs.notebook

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    October25,2016

    RECIPROCALFUNCTION:

  • 3.5RationalFunctionsandTheirGraphs.notebook

    4

    October25,2016

    Anotherbasicrationalfunctionis

  • 3.5RationalFunctionsandTheirGraphs.notebook

    5

    October25,2016

    VerticalAsymptote:Thelinex=aofthegraphofafunctionfiff(x)increasesordecreaseswithoutboundasxapproachesa.

    As As

    As As

  • 3.5RationalFunctionsandTheirGraphs.notebook

    6

    October25,2016

    LocatingaVerticalAsymptote:If isarationalfunctioninwhichp(x)and

    q(x)havenocommonfactorsandaisazeroofq(x),thedenominator,thenx=aisaverticalasymptoteofthegraphoff.

    Ex2:Findtheverticalasymptotes,ifany,ofthegraphofeachrationalfunction.

    a) b) c)

  • 3.5RationalFunctionsandTheirGraphs.notebook

    7

    October25,2016

    Note:Avaluewherethedenominatorofarationalfunctioniszerodoesnotnecessarilyresultinaverticalasymptote.Thereisaholeinthegraphatx=a,andnotaverticalasymptote,underthefollowingconditions:thevalueacausesthedenominatortobezero,butthereisareducedformofthefunctionsequationinwhichadoesnotcausethedenominatortobezero.(Thefactorxacancelsoutwhentherationalfunctionissimplified).

  • 3.5RationalFunctionsandTheirGraphs.notebook

    8

    October25,2016

    GobacktoEx2.Arethereanyfunctionsthathaveholesinthegraph?Identifywherethisoccurs.

  • 3.5RationalFunctionsandTheirGraphs.notebook

    9

    October25,2016

    HorizontalAsymptote:Theliney=bofthegraphofafunctionfiff(x)approachesbasxincreasesordecreaseswithoutbound.

    As

  • 3.5RationalFunctionsandTheirGraphs.notebook

    10

    October25,2016

    LocatingHorizontalAsymptotes:

    Letfbearationalfunctiongivenby:

    Thedegreeofthenumeratoris:________Thedegreeofthedenominatoris:_______

    1.

    2.

    3.

    Examples:

  • 3.5RationalFunctionsandTheirGraphs.notebook

    11

    October25,2016

    Ex3:Findthehorizontalasymptote,ifany,ofthegraphofeachrationalfunction:

    a) b) c)

  • 3.5RationalFunctionsandTheirGraphs.notebook

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    October25,2016

    UsingTransformationstoGraphRationalFunctions:

    Ex4:Usethegraphof tograph

  • 3.5RationalFunctionsandTheirGraphs.notebook

    13

    October25,2016

    Ex5:Usethegraphof tograph

  • 3.5RationalFunctionsandTheirGraphs.notebook

    14

    October25,2016

    Homework:MathXL:3.13.4Review

    Quiz(3.13.4)Tomorrow

    Page 1: Oct 25-7:39 AMPage 2: Oct 25-7:45 AMPage 3: Oct 25-7:48 AMPage 4: Oct 25-7:49 AMPage 5: Oct 25-7:49 AMPage 6: Oct 25-7:52 AMPage 7: Oct 25-7:55 AMPage 8: Oct 25-7:56 AMPage 9: Oct 25-7:56 AMPage 10: Oct 25-7:58 AMPage 11: Oct 25-8:00 AMPage 12: Oct 25-8:02 AMPage 13: Oct 25-8:03 AMPage 14: Oct 25-8:05 AM

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