1

AdvAlg Name:__________________________________ Date:__________________________Pd_______

AA2PRACTICETEST:TRANSFORMATIONS

I.MULTIPLECHOICE.Circlethecorrectanswer.1.Functionf(x)=x2ismovedoneunitright,andoneunitdownwillbewrittenas

a. f(x)=(x+1)2-1b. f(x)=(x-1)2-1c. (x)=(x-1)2+1d. (x)=(x+1)2+1

2.f(x)=!

!isreflectedoverthexaxisandmoved2upwillbewrittenas

a. f(x)=- !!!!

b. f(x)=!!

c. f(x)=–!!+ 2

d. f(x)=!!–2

3.Comparedwiththeparentoftheabsolutefunction,thefunctionf(x)=|-(x-6)|+3isbeingmoved

a. 6right,reflectedovery-axis,then3downb. 6left,reflectedoverx-axis,then3downc. 6right,reflectedovery-axis,then3upd. 6left,reflectedoverx-axis,then3up

4.Functiony=|x|istransformedintoy=8-|x–3|.Itisbeingmoved

a. 3leftandreflectedy-axis,8upb. 3rightandreflectx-axis,8upc. 3leftandreflectx-axis,8upd. 8left,3down,reflectedaboutthey-axis

5.Thegraphoff(x)=x2–5undergoesthetransformationf(x+2).Itsnewequationwillbe

a. (x+2)2–5b. x2–3c. x2+2d. (x-2)2–5

6.Giventhefunctionf(x+h)+k,bychangingthevalueofh,thefunctionwillmove

a. rightonlyb. uponlyc. upordownd. leftorright

7.Giventhegraphy=f(x-10)+12.Whenthisgraphistranslatedtwoleftandonedown,thenewequationis

a. y=f(x+2)+1b. y=f(x-12)–1c. y=f(x-8)+11d. y=f(x-8)+13

2

8.Giventhefunctionf(x+h)+k.Bychangingthevalueofk,thefunctionwillmove

a. leftorrightb. rightonlyc. upordownd. uponly

9.Thefunctionf(x)isbeingflippedoverthex-axis,itsformulafortransformationis

a. –f(x)b. 1–f(x)c. f(-x)d. f(x–1)

10.Thefunctionf(x)nowtransformintof(x)–10.Itisbeingmoved

a. 10upb. 10leftc. 10rightd. 10down

11.Theoriginalfunctionisf(x)=x3+5.Thetransformedfunctionisg(x)=x3–5.Itismoved

a. 5rightand5downb. 5downc. 5leftand5downd. 10down

12.Thetransformationon4f(x)isa….

a. Horizontalstretchb. Verticalstretchc. Horizontalcompressiond. Verticalcompression

13.Thefunctionf(x)istransformedintof(x–2)+4.Itisbeingmoved

a. Right2,up4b. Right4,down2c. Left4,up2d. Left2,up4

14.Theoriginalfunctionisf(x)= 𝑥 + 3! .Thetransformingfunctionisg(x)= 𝑥! +3.Itismoved

a. 3right,3upb. 3upc. 3left,3upd. 3left

15.Thetransformationonf(-x)is….

a. Ashifttotherightb. Reflectionaboutx-axisc. Ashifttotheleftd. Reflectionaboutthey-axis

3

16.Shiftingy=2xtotheleftby1unitanddownby9unitswouldyieldtheequation….

a. y=2x+1-9b. y=2x-9+1c. y=2x-1–9d. y=2x–9

17.Thedilationony=2 9𝑥is….a. Verticalcompressionbyafactorof2b. Horizontalcompressionby9c. Verticalstretchby18d. Verticalstretchby6

II.MATCHING.Matchtheequationwithcorrespondinggraph.

a. f(x)=xb. j(x)=x3

c. g(x)=2xd. m(x)=|x|

e. h(x)=x2f. p(x)= 𝑥!

g. k(x)= 𝑥

2.___________

3._________

4.__________

5.___________

6.___________

1.__________

7._________

4

III.READTHEDIRECTIONSFOREACHQUESTIONBELOW,THENANSWERTHEQUESTIONS.1. Writetheequationforthegraphofthefunctiong(x),obtainedbyshiftingthegraphoff(x)=x3nineunits

left,reflectingthatresultoverthex-axis,compressingthegraphverticallybyhalf,andshiftingthegraphupfourunits.

2. Describethetransformationsthatwouldproducethegraphofthesecondfunctionfromgraphofthe

parentfunction.

a.f(x)=xàg(x)=-½x-1_________________________________________________________________________________

b.f(x)=x2àg(x)=-(x+1)2________________________________________________________________________________

c.f(x)= 𝑥! àg(x)=3 −𝑥! +6__________________________________________________________________________

3.Writetheequationofthetransformedgraph.

5

IV.MATCHING

1.______________

2._________________

3.__________________

4.________________

5.________________

6._________________

7.___________

a. 𝑔(𝑥) = − !!"(𝑥 + 3)! − 2

b. ℎ(𝑥) = 2√𝑥 + 5! + 1

c. 𝑗(𝑥) = 4(𝑥 − 3)! + 2

d. 𝑚(𝑥) = − !!(𝑥 − 3)! − 2

e. 𝑛(𝑥) = !! √𝑥 + 5! + 1

f. 𝑝(𝑥) = 4(𝑥 + 3)! + 2

g. 𝑟(𝑥) = !!√𝑥 − 5! + 1