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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