Kuta Software - Infinite Precalculus
Name___________________________________
Transformations of Graphs
Date________________ Period____
Describe the transformations necessary to transform the graph of f ( x) (solid line) into that of
g( x) (dashed line).
1)




2)
y











 x




y











 x
Describe the transformations necessary to transform the graph of f ( x) into that of g( x).
3) f ( x) x
g( x) x
4) f ( x)x 

g( x)( x)
Transform the given function f ( x) as described and write the resulting function as an equation.
5) f ( x)x 
expand vertically by a factor of 
translate down  units
7) f ( x) x
expand horizontally by a factor of 
translate right  unit
translate up  units

x
compress horizontally by a factor of 
translate left  units
6) f ( x)
8) f ( x) x
compress vertically by a factor of 
reflect across the x-axis
translate right  units
translate down  units
-1©Q s2u0b1z6M uKMuBtgaT rSVoEfdt\wuaUreeb vLILkCh.c _ ZAHlMlP trtiBg^hDtjsh CrzeYsKeXrcvcehdz.` y MMIaudaeN gwAi]t^he yIYnwfoiWnWiOtAeE xPNrsepcoaclOcXu]lguRsZ.
Worksheet by Kuta Software LLC
Write g( x) (dashed line) in terms of f ( x) (solid line).
9)














 x










12)
y











 x



y






11)

10)
y









 x



 x


 x
y



Identify the parent function f ( x) and write an equation for the function given.
13)




14)
y











 x




y









-2©A [2[0g1x6F SKQustAal hSAoZf`tMw]alrAeT LLELvCN.J F fA`lTln jreiwgphxtOsq \rbebsyeurAvqeXdQ.p V \MHaEdOel hwniZtyhU HIgnWfliQnnittKeN yParZeScQapl^cRualYuQse.
Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Name___________________________________
Transformations of Graphs
Date________________ Period____
Describe the transformations necessary to transform the graph of f ( x) (solid line) into that of
g( x) (dashed line).
1)




2)
y











 x




y











 x
compress vertically by a factor of 
translate up  units
reflect across the x-axis
translate left  units
Describe the transformations necessary to transform the graph of f ( x) into that of g( x).
3) f ( x) x
g( x) x
4) f ( x)x 

g( x)( x)
expand vertically by a factor of 
translate left  unit
expand vertically by a factor of 
reflect across the x-axis
translate down  unit
Transform the given function f ( x) as described and write the resulting function as an equation.
5) f ( x)x 
expand vertically by a factor of 
translate down  units

x
compress horizontally by a factor of 
translate left  units
6) f ( x)

g( x)x 
g( x)
7) f ( x) x
expand horizontally by a factor of 
translate right  unit
translate up  units
g( x)

( x) 


( x)
8) f ( x) x
compress vertically by a factor of 
reflect across the x-axis
translate right  units
translate down  units
g( x)


x
-1©P T2a0w1B6D nKjuEtha` PSXoFfXtqwEaorEeC ALrLOCD.R F vAolrlI QrXijgrhrtRso yrJe[sLeUrbvdeMdL.m c wMQaedDe] dwWimtphS tIdnkfDiZnMixteec sPfrbeqcOaOltczuolauksz.
Worksheet by Kuta Software LLC
Write g( x) (dashed line) in terms of f ( x) (solid line).
9)




10)
y











 x











11)



g( x) f (( x))


g( x) f









 x




 x



 x


 x
y









g( x) f ( x)


x 




( )
12)
y
y
g( x) f ( x)
Identify the parent function f ( x) and write an equation for the function given.
13)




14)
y











 x













Parent: f ( x) x

g( x) ( x)

y
Parent: f ( x)x 

g( x)x 
Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com
-2©P X2u0l1B6W DKWuAtaam nSpoAfltzwaadrCeu VL]LMCA.u E yABl]lh ArViOgjhrtssl erlexsqe_ravcead^.N P _MhaNdceh Pwbiutkhy GI]nSftienViRteeK JPCrCeZcyaplLc^uzlEursh.
Worksheet by Kuta Software LLC