Graphing Radical Functions

Graphing Radical Functions Essential Question How сап you identify the domain and range of а radical function? EXPLORATION: Identifying Graphs of Radical Functions Work with а partner. Match each function with its graph. Then identify the domain and range of each function. 1. ✓х f(x) = 2. f(x) = ¼ 6\ t '"'· i:,r'"""" I в. А. 4 f(x) =-¼ з. 4. f(x) l 1 с. D. 4 4 -6 6 -6 -4 6 -4 -4 1..' EXPLORATION: Identifying Graphs of Transformations Match each transformation of f(x) = 5. g(x) = .Jх + 2! JePI--Z. ,·1 ,J' ,1 6 -4 g(x) = � г.....·1 в. 4 -6 6. ✓х with its graph. Then identify the domain and range of each function. 7. g(x)=✓x+2 -.,_2 в (1'5j,)+ - '2- -6 i�+./-"L 6 1 i�t+- 2 (_ )L• -,,, . : rц{( c,,h'-in\ о/ 4 / 6 -6 -4 ---- g(x) = -.Jx + 2 , С. 4 8. -4 г - ·1 ,. (i. � � 1 . : ( ' 1 ' 1/ .• .,,,. t9t"\ )С -�-r,:1-J 4 � -6 -4 6 ln your own words, write the meaning of each vocabulary term. radical function --- J� �--·� L �•,\ \.; Core Concepts Parent Functions for Square Root and Cube Root Functions The parent function for the family of square root functions is f(x) = ✓х -4 . �;_ The parent function for the family of cube root functions isf(x) = ½. i· (,, - -2 � �у 2 -4 = � =� ..,,,;;;;;. - .J.-� ,,,.. ( 1, 1 О, О) N -2 .,,,,, 2 4 ', � х -1-v]2. -1, -1) 1 lf Domain: х � О, Range: у � О . ,,, :·· Со - Domain and range: AII real numbers "�) -.1' ·� ' ( - -"j'" Transformation Horizontal Translation Grapl1 shifts left or right. f(x Vertical Translation Grapl1 shifts up or down. Retlection Grap/1 flips over х- or y-axis. Examples f{x) Notation - h) f(x) + k :{ -� J(-x) ·i�• -f(x) g(x) = � 2 units right g(x) = � 3 units left g(x) = ✓х + 7 7 units up g(x) = ✓х 1 unit down g (x ) = - Fx g(x) = -.j; 1 ( s;),�. ,/ in the y-axis in the x-axis J ( • . ·, \ 1,. �· ) ,' Horizontal Stretch or Shrink Graph stretches away from or shrinks toward y-axis. Ve1·tical Stretch or Shrink Grap/1 stretches away from or sl1rinks toward x-axis. - ).�-J ',' f(ax) /-,� J L -,'. _. r ✓ { -- ); ., а• f(x) ' ri ., '> ½ g(x) = .,& shrink Ьу а factor of g(x) = stretch Ьу а factor of 2 JF g(x) = 4✓х stretch Ьу а factor of 4 g(x) = shrink Ьу а factor of ½✓х ½ \ ) __,/ Extra Practice Graph the function. ldentify the domain and range of each function. 1. .r,/ i /(х) 1 -�i ,, \__ � :--::-; = � + 1 � tл 1 \ ' / on у-�Х. ,:, '\ 5/1,i'tJ -·1 -'2 I 2 ? 2. ,___..�--.'3/ 3 {()) 3 Vr;�· �-' �� -t \ 2�0� 1 \ '2 \ & 1 '?. t '-'f l[ I о t Ь1 -ЬJ-�(-j') + 1 3.о� -\ � tt: ,f 1 -1 ( о -1 / -\ Lf �( - .. � 1 1 - \, О � g ( х) = 2 х - )'1 2 - 4 )( ... '5' rr--s и+ � 1.1 1/ S- ol...oi'-"'I', ...,j У--- • '--· -- {1 -� \ 1 /.1 • ',) ' / �( б -/...,/ 1 ' ь 1 --7-.. 7 -1,1 7 % -�5 "'( °'· о -kt.. foy 2 V er-h'L4 l � � - Lf z ' -s2 Г� - 2--( ') - L-1 � у 1.- - 1--( '2.. �- 7-,;; z.. ( 1. 1-11 ч\ - '2 �-"?, - �, -L.( - t( 1 :Z. (1,7� �, "1 ь - 1..r L 2 r2- - �1 1 2 r�-5·· L. ( 1 2 v'Cf-s· '2- г:т 2- {'2') 1.., { - '-/ -· '-/ - ( ir '2-Jч-) Ft -i/ -Е- evtk) ; L"� �r; dд / 1 / ,"t'f 1'� с)· J(де� Di?,rФ\; ; х � 5 (\ �cr,�e.: '/ ?.-Ч Graph the function. ldentify the domain and range of each functio n. з.f(х) = - ✓х Ч- 3 1 +2 ,_ le-?+- 3 ир 7- Of\ о [,,,r�IJГ �....,.. -, - � Z- -t 'Z. � ( 1, 1.-1 \)'f 'Z.. ,z_ - ,t. 1 ·:,, -Jz�:� + г. - ,ЧS" ,_ - -3 - Г5 .+-'Z. - (i,1.3} +,� - Го -J-\ +., 1· 2. - о t2 + 1. --( oyr 2. о+-� 4· 1. - Гъ +1,, ... (\,,";"')+-Z.. г--·-·• ---· -,J3-t1 + 2,. - rr; t-2. r,�ht 3 - - ,-.r- . loo�i� "f -J\ + i -(1\+2.. 1 + ...,) t 2 -.г;;г +- -z.. 'Ооме,,; \1\-. '"�Р� � � ._ { '2--) +- "L -· v' - Ч+1 r=r t· '- +� v ax ,rt: .f-(ec+ ol\ у-"' )(iS h ori 't;OV\ k I shr, fltc'by � ' 6.[лх) = ..... L - J--z..+3 + 2- -('2.,L-/�)-1 2., "' ( z..�5\�· '2. Describe the transformation of /(х) Ьу represented Ьу g(x) ---- -- ·---- -4.[/(х) = VX · g(x) = 1/х - -t- 4 s.\f(x) = 1/х ; g(x) = .. - 1--1-- - 1 �� '-'- -Г� .::� .1.. i кr.....r- Х- С,\ Х i.S - J-Ч + 3 +2 ··\ - 1-- r е_ .Р, tL.c.:/- - 2. ' бх + s1 g(x) = iбх - 5. rt i.vf\%-fV\ -Lfh e'f-p\�;r'IS +-5] ·t е.,11 1 , . -3 Write а rule for g from the transformations. 8. g is а horizontal stretch Ьу а factor of З followed Ьу а translation 6 u11its to the rigl1t of thegraph of Гх f(x) = 1 S�i'�- W\ * ---_..-iJ V\ 11--L � "'- d 4 � t-rt1 fo., -Р ( � х -�) d . ' \ -;(:>;;) � J½t< -" V\ s �J 10. g is а horizontal shrink Ьу а factor of f(x) = T{l1sx + 1. 1 f}\ � �,, t'r1 s 9. g is а translation 7 le , followed Ьу а retl ti 1 ontl1 ·-a'i of thegraph of f(x) (Vxj - +-(?<-tlJ $и[,§�-� ?( �;] i followed Ьу а translatio11 1 О ttnits to the Left. of tl1e grapJ1 of 11