7.4 part 2 p. 502-503

 +<B0.;B@2A526;C2?@2?29.A6<;@56=
/2AD22;2E=<;2;A6.9.;19<4.?6A5:603B;0A6<;@A<4?.=59<4.?6A5:603B;0A6<;@
&YUSB&YBNQMF
$
'RAPHTHEFUNCTION
ALOGX
&6*286&4-7+363,&6.8-1.(92(8.327
(524?.=5<3 9<4 6@@5<D;/29<D3<? .;13<? 20.B@2
9<4 .;1 .?26;C2?@23B;0A6<;@A524?.=5<3 9<4 6@A52?23920A6<;<3A524?.=5<3 6;A5296;2 .-& ,$ ),% $,. .-&,$ ),% $,. BYLOGX
),% $<A2A5.AA52 .E6@[email protected]?A60.9.@F:=A<A2<3A524?.=5<3 9<4 (521<:.6;<3 9<4 6@ .;1A52?.;[email protected]?2.9;B:/2?@
#
,FZ2VFTUJPOUP"TLGPS
&YBNQMF
9<4 OFANYLOGARITHMICFUNCTIONOFTHE
FORMYLOGBX AND B
9<4
3098.32
%9<A@2C2?.90<;C2;62;A=<6;A@
"MHFCSB
DMBTT[POFDPN
!N!NIMATED!LGEBRAACTIVITYIS
AVAILABLEONLINEFOR%XAMPLE
4HISACTIVITYISALSOAVAILABLEONTHE
0OWER0RESENTATIONS#$2/-
"WPJEJOH$PNNPO&SSPST
6&4-03,&6.8-1.(+92(8.327
'%)*#) $#
s7HATTWOPOINTSAREONTHEGRAPH
3OMESTUDENTSMAYHAVETROUBLE
MAKINGATABLETOVALUESTOUSEFOR
GRAPHINGALOGARITHMICFUNCTION
"ECAUSESTUDENTSATTHISPOINTARE
MOREFAMILIARANDCOMFORTABLEWITH
EXPONENTIALFUNCTIONSTHANLOGARITH
MICONESSHOWTHEMHOWTHEY
CANUSEWHATTHEYALREADYKNOW
3UGGESTMAKINGATABLEOFVALUESBY
CHOOSINGTHEY VALUESFIRSTUSING
CONSECUTIVEINTEGERSANDTHENFIND
INGTHECORRESPONDINGX VALUESTO
FORMTHEORDEREDPAIRS!SIMILAR
APPROACHISTOCONSTRUCTATABLE
FORTHECORRESPONDINGEXPONENTIAL
FUNCTIONANDTHENTOREVERSEXANDY
INEACHPAIRTOFINDORDEREDPAIRSFOR
THELOGARITHMICFUNCTION
),% @B05.@ .;1 (52 .E6@6@.
C2?A60.9.@F:=A<A2
?<: A< 1?.D.0B?C2
A5.A@A.?A@7B@AA<A52?645A<3A52
.E6@.;1:<C2@B=A5?<B45
A52=9<AA21=<6;A@.@@5<D;
/29<D
?<: A< 1?.D.0B?C2
A5.A@A.?A@7B@AA<A52?645A<3
A52 .E6@.;1:<C2@1<D;
A5?<B45A52=9<AA21=<6;A@.@
@5<D;/29<D
"MHFCSB
%9<A@2C2?.90<;C2;62;A=<6;A@
@B05.@.;1
(52 .E6@[email protected]?A60.9
.@F:=A<A2
&%%,"!"
#&$ *#"!!&!"$& '!&"!%
%JGGFSFOUJBUFE*OTUSVDUJPO
7JTVBM-FBSOFST 2EINFORCETHEINVERSERELATIONSHIPBETWEEN
YLOGBXANDYBXBYHAVINGSTUDENTSGRAPHTHEREmECTIONIN
THELINEYXOFEACHOFTHEGRAPHSIN%XAMPLE(AVESTUDENTS
WRITEANDGRAPHEACHINVERSEFUNCTIONANDCOMPAREEACHGRAPH
TOTHEGRAPHOFTHEREmECTION
3EEALSOTHE!LGEBRA4OOLKITFORMORESTRATEGIES
+<B0.;4?.=5.9<4.?6A5:603B;0A6<;<3A523<?:
9<4 /FA?.;@9.A6;4A524?.=5<3A52=.?2;A3B;0A6<; 9<4 #
&YUSB&YBNQMF
6&270&8*&03,&6.8-1.(,6&4-
'RAPHYLOGX3TATETHE
DOMAINANDRANGE DOMAINX
RANGEALLREALNUMBERS
'% !$ )))$" ##'#
3098.32
),%
3B;0A6<; 9<4 D5605=.@@2@
A5?<B45.;1
B;6A@.;1B=B;6A(52A?.;@9.A21
4?.=5=.@@2@A5?<B45
.;1(524?.=5@.@F:=A<A26@
(521<:.6;6@ .;1
A52?.;[email protected]?2.9;B:/2?@
),%
,FZ2VFTUJPOUP"TLGPS
&YBNQMF
s$OTRANSLATIONSOFALOGARITHMIC
'%)*#) $#)))$" ##'# 8##*.%'+$,..0
",*'+ .+%#)).#)+1* #./
9<4
#
9<4 ",*'+ .+%#)).#)+1* #./
",*'+ .+%#)).#)+1* #./
"
$
" '&(')/*&
! $ <=F.;10<:=92A29<4.?6A5:D6A5/.@[email protected].; 9<4.?6A5: !,**,+
" A52?29.A6<;@56=/2AD22; .;1 9<4 &#$1+!0',+/.#
'+2#./#/,$#!&,0&#.
#
# ,' ))&*) $# #-%$##) !$'"
"!#
"$*%.
9<4 9<4 9<4 $ .;10<??20AA522??<?6;
6;9<4.?6A5:603<?:
?2D?6A6;4A522>B.A6<; ##*.%'+
9<4 #
! +!*))!$' )", )$*)*( #!*!)$'
"!#
"$*%.
9<4 9<4 9<4 9<4 9<4 9<4
9<4 9<4 9<4
9<4 9<4 9<4 ('&"$& %!$#"$& '!&"!%
'UIDED0RACTICE
(AVESTUDENTSSUMMARIZETHEMAJOR
POINTSOFTHELESSONANDANSWERTHE
%SSENTIAL1UESTION7HATISTHE
RELATIONSHIPBETWEENEXPONENTIAL
ANDLOGARITHMICFUNCTIONS
s4HEEQUATIONSLOGBYXLOGARITH
MICFORMANDBXYEXPONENTIAL
FORMAREEQUIVALENT
s4HEGRAPHOFALOGARITHMICFUNC
TIONRISESFROMLEFTTORIGHTIFB
ANDFALLSFROMLEFTTORIGHTIF
B4HEGRAPHHASAVERTICAL
ASYMPTOTE
%XPONENTIALANDLOGARITHMIC
FUNCTIONSWITHTHESAMEBASEARE
INVERSES
3AMPLEANSWER4HEAND]z
ARESWITCHEDAROUNDLOG]z
GRAPHAFFECTTHEDOMAINANDOR
THERANGE%XPLAIN !HORIZONTAL
TRANSLATIONAFFECTSTHEDOMAIN
BUTNOTTHERANGE!VERTICAL
TRANSLATIONDOESNOTAFFECTTHE
DOMAINORRANGESINCETHERANGE
ISALWAYSALLREALNUMBERS
$MPTJOHUIF-FTTPO
%
/*
&
')/%($*&
9<4 )&*$+ A52=.?2;A4?.=5923A
#+! A524?.=5<3A52=.?2;A