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8.2LogarithmGraphs-BasicsofLogarithmicGraphsVerticalAsymptote:X-Intercept:Y-Intercept:EndBehavior:Whathappenstothegraphwhenwechangedifferentpartsofthefunction?a: b: c:

NOTES

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Describetheshiftsofthegivengraphs.Ex1:Ex2:Ex3:Forthefunction,findthex-intercept,verticalasymptotes,endbehavior,describeanyshiftsandthensketchthegraph.Ex4:YOUTRY!

SUMMARY:

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8.2LogarithmGraphs

Directions:Describetheshiftsofthegraphforeachequation,incomparisontoitsbasefunction.1)f x = ln 𝑥 − 2 − 3

2)𝑓 𝑥 = log 𝑥 + 5 3)𝑓 𝑥 = log! 𝑥 + 5 − 4

Directions:Findthex-interceptsofthefollowingfunctions.4)𝑓 𝑥 = log! 𝑥 + 1 − 2

5)𝑓 𝑥 = log! 𝑥 − 3 + 2 6)𝑓 𝑥 = log 𝑥 − 5 − 1

Directions:Findtheverticalasymptoteofthegraphforeachequation.7)𝑓 𝑥 = log! 𝑥 + 10 − 2 1

8)𝑓 𝑥 = log! 𝑥 − 4 − 2 9)𝑓 𝑥 = ln 𝑥 − 3

Directions:Findtheendbehaviorofthefollowingfunction.10)𝑓 𝑥 = log! 𝑥 + 4 − 12

11)𝑓 𝑥 = ln 𝑥 + 7 − 10

Directions:Forthegivenfunction,findthex-intercept,verticalasymptote,endbehavior,describeanyshiftsandthensketchthegraph.12) 𝑓 𝑥 = log 𝑥 − 1 + 3x-intercept:EndBehavior:Sketch:VerticalAsymptote:Shifts:

PRACTICE

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13)𝑓 𝑥 = log! 𝑥 + 8 − 4x-intercept:EndBehavior:Sketch:VerticalAsymptote:Shifts:14)𝑓 𝑥 = log! 𝑥 − 2x-intercept:EndBehavior:Sketch:VerticalAsymptote:Shifts:Findthediscriminant.Statethenumberandnatureofthesolutionsforeachquadraticbelow.15) 10𝑟! − 9𝑟 − 8 = −10 16) −9𝑎! − 4 = −5𝑎

8.2LogarithmicGraphs

Directions:Forthegivenfunction,findthex-intercept,verticalasymptote,endbehavior,describeanyshiftsandthensketchthegraph.1) 𝑓 𝑥 = log 𝑥 − 1 + 3x-intercepts:EndBehavior:Sketch:VerticalAsymptote:Shifts:

WRAP UP

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2)Calculatorscanbeusedtocomeupwithequationsthatmodeldata.ThisiscalledREGRESSION.YoulearnedhowtodoregressioninAlgebraI,butifyouforgotorneedarefresher,usethevideoonwww.flippedmath.cominthissectiontohelpfindtheregressionforthegivendataandthenusethemodeltoanswerthefollowingquestions.In2013,theAlgebrosformedandstartedmakingthewebsitewww.flippedmath.com.Theystruggledatfirsttogetvisitorstocomeseetheiramazingpage.Belowisatableofvalues.WeeksOnTheInternet AverageNumberofHitsPerDayfortheWeek.1 5.12 6.53 7.64 8.35 8.7a)Sketchandlabelascatterplot(withscale)below.Makesureyouidentifywhatyourx,andy-valuesareinthesituation.b)ExplainWHYyouthinkthisscatterplotmayberepresentedbyaLOGARITHMICGRAPH.c)Findthelogarithmicregressionthatbestmodelsthissituation.ThereisnoLogReg,soyouneedtousetheoneforNATURALLOG(LnReg).Roundyourvaluestohundredths.d)Accordingtoyourmodel,howmanyaveragehitsperdaywilltherebeduringweek10?Week20?After1year?After5years?e)HowmanyweekswillittakebeforetheAlgebrosaveragenumberofhitsperdayisabove20?EXPLAINhowyousolvedit.

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EXIT TICKET –

For the function 𝑔(𝑥) = log(𝑥 − ℎ), what value of h will cause the function to pass through the

point (4, 1)?

Explain your solution TWO different ways?

Algebraically:

Graphically: