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#OPYRIGHT-C$OUGAL,ITTELL(OUGHTON-IFFLIN#OMPANY ,ESSONs!LGEBRA.OTETAKING'UIDE
'OAL +'RAPHSQUAREROOTFUNCTIONS
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2ADICALEXPRESSIONii>V>>>`V>]V>>>i]VLi]i
2ADICALFUNCTION>`V>vVV`i>>`V>iii`ii`i>>Lii>`V>`
3QUAREROOTFUNCTION>`V>vV>V>>>i
0ARENTSQUAREROOTFUNCTIONq]z
'RAPH3QUARE2OOT&UNCTIONS
0!2%.4&5.#4)/.&/2315!2%2//4&5.#4)/.34HEMOSTBASICSQUAREROOT
FUNCTIONINTHEFAMILYOFALLSQUAREROOTFUNCTIONSCALLEDTHE >i>ivV ISY q
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4HEGRAPHOFTHEPARENTSQUAREROOTFUNCTIONISSHOWN
9OUR.OTES
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,ESSONs!LGEBRA.OTETAKING'UIDE #OPYRIGHT-C$OUGAL,ITTELL(OUGHTON-IFFLIN#OMPANY
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'RAPHTHEFUNCTIONYq]zXANDIDENTIFYITSDOMAIN
ANDRANGE#OMPARETHEGRAPHWITHTHEGRAPHOFYq]zX
3OLUTION3TEP-AKEATABLE"ECAUSETHE
SQUAREROOTOFANEGATIVENUMBERIS `ivi` XMUSTBENONNEGATIVE3OTHEDOMAINIS q
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3TEP0LOTTHEPOINTS
3TEP$RAWA Vi THROUGHTHEPOINTS&ROMEITHERTHETABLEORTHEGRAPHYOUCANSEETHERANGEOFTHEFUNCTIONIS a
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4HEGRAPHOFYq]zXISVERTICAL iV BYA
FACTOROF { ANDA iviVi> OF THEGRAPHYq
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%XAMPLE 'RAPHAFUNCTIONOFTHEFORMYAq]zX
'RAPHTHEFUNCTIONYq]zXANDIDENTIFYITSDOMAIN
ANDRANGE#OMPARETHEGRAPHWITHTHEGRAPHOFYq]zX
3OLUTION4OGRAPHTHEFUNCTIONMAKEATABLE
THENPLOTANDCONNECTTHEPOINTS4HEDOMAINIS q
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Y
4HERANGEIS q 4HEGRAPHOFYq
]zXISA iV>>> OF UNITS
` OFTHEGRAPHOFYq]zX
%XAMPLE 'RAPHAFUNCTIONOFTHEFORMYq]zXK
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#OPYRIGHT-C$OUGAL,ITTELL(OUGHTON-IFFLIN#OMPANY ,ESSONs!LGEBRA.OTETAKING'UIDE
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}>q]z
Yq]zX
>\q,>}i\q{/i}>>iV>>>v{
vi}>q]z
#HECKPOINT 'RAPHTHEFUNCTIONANDIDENTIFYITSDOMAINANDRANGE#OMPARETHEGRAPHWITHTHEGRAPHOFYq
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'RAPHTHEFUNCTIONYq]zXANDIDENTIFYITSDOMAIN
ANDRANGE#OMPARETHEGRAPHWITHTHEGRAPHOFYq]zX
3OLUTION4OGRAPHTHEFUNCTIONMAKEATABLE
THENPLOTANDCONNECTTHEPOINTS4OFINDTHEDOMAINFINDTHEVALUESOFXFORWHICHTHERADICANDXIS i}>i 4HEDOMAINIS qx
X
Y {
4HERANGEIS q 4HEGRAPHOFYq]zXIS
A >>> OF x UNITSTOTHE iv OFTHEGRAPHOFYq
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%XAMPLE 'RAPHAFUNCTIONOFTHEFORMYq]zXH
-
,ESSONs!LGEBRA.OTETAKING'UIDE #OPYRIGHT-C$OUGAL,ITTELL(OUGHTON-IFFLIN#OMPANY
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4OGRAPHAFUNCTIONOFTHEFORMYAq]zXHK
YOUCANFOLLOWTHESESTEPS3TEP 3KETCHTHEGRAPHOFYAq
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YAq]zXSTARTSATTHE } ANDPASSES
THROUGHTHEPOINT ]>
3TEP 3HIFTTHEGRAPH{H{UNITS > TOTHE RIGHTIFHIS i ANDTOTHELEFTIFHIS i}>i AND{K{UNITS iV> IFKISPOSITIVEAND ` IFKISNEGATIVE
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3TEP3KETCHTHEGRAPHOF
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3TEP3HIFTTHEGRAPH{H{UNITS HORIZONTALLYAND{K{UNITS
VERTICALLY.OTICETHATH ANDK 3HIFTTHEGRAPH } AND
%XAMPLE 'RAPHAFUNCTIONOFTHEFORMYzAq]zXHzzK
'RAPHTHEFUNCTIONYq]zX
ANDIDENTIFYITSDOMAINANDRANGE#OMPARETHEGRAPHWITHTHEGRAPHOFYq
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)DENTIFYTHEDOMAINANDRANGEOFTHEFUNCTIONIN%XAMPLE
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#HECKPOINT #OMPLETETHEFOLLOWINGEXERCISES