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

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• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

3.5:RationalFunctionsandTheirGraphs Date:10/25

RationalFunctionsarequotientsofpolynomialfunctions.Thismeansthatarationalfunctioncanbeexpressedas:

Wherepandqarepolynomialfunctionsand

Thedomainofarationalfunctionisthesetofallrealnumbersexceptthexvaluesthatmakethedenominatorzero.

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

Ex1:Findthedomainofeachrationalfunction.(Useintervalnotation)

a) b) c)

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

RECIPROCALFUNCTION:

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

Anotherbasicrationalfunctionis

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

VerticalAsymptote:Thelinex=aofthegraphofafunctionfiff(x)increasesordecreaseswithoutboundasxapproachesa.

As As

As As

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

LocatingaVerticalAsymptote:If isarationalfunctioninwhichp(x)and

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

Ex2:Findtheverticalasymptotes,ifany,ofthegraphofeachrationalfunction.

a) b) c)

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

GobacktoEx2.Arethereanyfunctionsthathaveholesinthegraph?Identifywherethisoccurs.

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

HorizontalAsymptote:Theliney=bofthegraphofafunctionfiff(x)approachesbasxincreasesordecreaseswithoutbound.

As

• 3.5RationalFunctionsandTheirGraphs.notebook

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October25,2016

LocatingHorizontalAsymptotes:

Letfbearationalfunctiongivenby:

Thedegreeofthenumeratoris:________Thedegreeofthedenominatoris:_______

1.

2.

3.

Examples:

• 3.5RationalFunctionsandTheirGraphs.notebook

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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

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October25,2016

Ex5:Usethegraphof tograph

• 3.5RationalFunctionsandTheirGraphs.notebook

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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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