WelcomeAcceleratedAlgebra2!Tear-Out:Pgs.329-340(classnotes) Pg.342(homework)

U5H5:Pg.342#11-13,15,16(doparentinadifferentcolor),19-22Updates:U5Q2willbeJanuary30th

U5TwillbeFebruary6th

(1) ExponentialGraphs(21-3/21-4/21-5)(2) Closure

Agenda

IwillleaveonepageblankformynextsetofSBnotes.

Today’sLesson#:21-3,21-4,21-5Topic:ExponentialGraphsLO#6:Transformanddescribecharacteristicsofanexponentialgraph.

Notebook!

Pg.329 Do#1intheMyNotesColumn.Thenanswer#2-3.Comparewithyourtablemates.(2mins)

21-3ExponentialGraphsandAsymptotes

Whattellsusanexponentialfunctionincreasesvs.decreasesjustbylookingattheequation?

Pg.329 ReadandhighlighttheimportantinformationinthenexttwoparagraphsandreadtheMATHTERMSbox.

21-3ExponentialGraphsandAsymptotes

Asymptoteo  Anasymptoteisalinethatthegraphofthefunctionapproaches.

o  Asthegraphofthefunctionapproachesin\inity(ornegativein\inity)thefunctioncurvegetscloserandclosertotheasymptotewithouttouchingit.

Note:WewilllearnthatyoucancrossaHAorSAlater,butthentheywillcontinuetogetcloserandcloserin:initely.

21-3ExponentialGraphsandAsymptotes

Pg.329 Wewillcomplete#4(a-b)asaclass.Independentlydo#5(a-b)-6.(1min)

21-3ExponentialGraphsandAsymptotes

Whattellsusthey-interceptofanexponentialfunctionbylookingattheequation?

Pg.331 Wewilldo#1atogetherandplot3speci\icpoints.Do#1bandcomparewithyourdiagonalpartner.(1min)

21-3ExponentialGraphsandAsymptotes

Pg.332 Youwilldo#2aand#2cinyourgroups.Yesplot3points.Dointhreedifferentcolors.

21-3ExponentialGraphsandAsymptotes

ExponentialParentFunctiono  Exponentialparentfunctionisy=bxwherebisaconstant.o  Ifb>1thefunctionisincreasing.o  If0<b<1thefunctionisdecreasing.

21-3ExponentialGraphsandAsymptotes

21-3ExponentialGraphsandAsymptotes

y = −a(bx−c )+ d

+MoveUp-MoveDownHorizontalAsymptotey=d

+Moveleft-Moveright

VerticalStretchifa>1Comp.if0<a<1Y-intercept(0,a)

Ref.acrossx-axis

Pg.333 Complete#3(a-b)inyourgroups.Includetheparentgraphinadifferentcolor.

21-3ExponentialGraphsandAsymptotes

Pg.334Do#cand#4.Includetheparentgraphinadifferentcolor,domain,range,asymptote,anddescribethetransformations.

21-4TransformingExponentialFunctions

Thenumbereisafamousirrationalnumber,andisoneofthemostimportantnumbersinmathematics.The\irstfewdigitsare

2.7182818284590452353602874713527…

ItisoftencalledEuler'snumberafterLeonhardEuler.eisthebaseofthenaturallogarithms(inventedbyJohnNapier).

(Itiscalledthenaturalbasesinceyouareabletotakeitsderivativeandyoustillreceivethesamefunction.~forthosewhowereinterested)

21-5NaturalBaseExponentialFunction

TheNumbere(NaturalBase)o  Representedbythelettere=2.7182818…o  Isexpressedbythefunctiony=ex.Yes,eisexponential!

Usingyourgraphingcalculatorsketchy=exinyournotebook,thenanswerthefollowingquestions:•  Whatisthey-intercept?•  Whatistheasymptote?

21-5NaturalBaseExponentialFunction

Pg.337Wewilldo#4atogether.Do#4binyourgroups!(2mins)

21-5NaturalBaseExponentialFunction

Pg.338Do#5cindependently.(2mins)Comparewithanyoneelseintheroomthatisnotatyourtable.

21-5NaturalBaseExponentialFunction

Pg.339Do#7-10withyourhorizontalpartner.(2mins)

21-5NaturalBaseExponentialFunction

Identifytheparentfunctionandlistthetransformations.Whatisthehorizontal

asymptote.

Y=-0.3(e)x-4

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