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
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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
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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
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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
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Worksheet by Kuta Software LLC
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