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Parent Function Transformations
( )f x x
( )f x mx b
Linear
Parent Function
Transformation Function
Translation (b)
Move down 4 unit
( ) 4f x x
b moves up or down
( )f x mx b Linear
Transformation Function
Stretch (m)
Stretch by a factor of 2
( ) 2f x xCompression (m)
1( )
4f x x
Compressed by a factor of 14m stretch and compress
( )f x mx b Linear
Transformation Function
reflection (m)
Reflect over the x-axis
( )f x x
m reflection
2( )f x a x h k
( )f x a x h k
( )f x a x h k
3( )f x a x h k
1( )f x a k
x h
Transformation Function
a ---stretch ---compression ---reflect over x-axis
h ---moves left or right ***opposite***
k ---moves up or down
Quadratic
Horizontal Translation (h)
Move left 2 units
2( ) 2f x x
h moves left or right
2( ) 4f x x Move right 4 units
vertical Translation (k)
Move down 2 units
2( ) 2f x x
k moves up or down
2( ) 5f x x
Move up 5 units
Quadratic
stretch (a)
Stretch by a factor of 2
2( ) 2f x xCompression(a)
compressed by a factor of
1
2
21( )
2f x x
reflection (a)2( )f x x
Reflect over the x-axis
Square Root
Move left 5 units
( ) 5f x x ( ) 4f x x
Move right 4 unit
h moves left or right
Move up 3 units
( ) 3f x x ( ) 8f x x
Move down 8 units
k moves up or down
Stretch by a factor of 2
( ) 2f x x
compressed by a factor of 1
4
1( )
4f x x ( )f x x
Reflect over the x-axis
2( )f x x 2( )f x a x h k
QuadraticParent Function
Transformation Function
Horizontal Translation (h)
Move left 2 units
2( ) 2f x x
h moves left or right
2( ) 4f x x Move right 4 units
2( )f x a x h k
Quadratic
Transformation Function
vertical Translation (k)
Move down 2 units
2( ) 2f x x
k moves up or down
2( ) 5f x x
Move up 5 units
2( )f x a x h k Quadratic
Transformation Function
stretch (a)
Stretch by a factor of 2
2( ) 2f x xCompression(a)
compressed by a factor of
1
2
21( )
2f x x
reflection (a)2( )f x x
Reflect over the x-axis
( )f x xSquare Root
Parent Function
Transformation Function
Horizontal Translation (h)
Move left 5 units
( )f x a x h k
( ) 5f x x ( ) 4f x x
Move right 4 unit
h moves left or right
Square Root
Transformation Function
vertical Translation (k)
Move up 3 units
( )f x a x h k
( ) 3f x x ( ) 8f x x
Move down 8 units
k moves up or down
Square RootTransformation Function
stretch (a)
Stretch by a factor of 2
( ) 2f x xCompression (a)
compressed by a factor of 1
4
1( )
4f x x
reflection (a)
( )f x x
Reflect over the x-axis
( )f x a x h k
( )f x xAbsolute Value
Parent Function
Transformation Function
Horizontal Translation (h)
Move right 5 units
Move left 2 unit
h moves left or right
( )f x a x h k
( ) 5f x x
( ) 2f x x
Absolute Value
Transformation Function
vertical Translation (k)
Move up 2 units
Move down 4 units
k moves up or down
( )f x a x h k
( ) 2f x x
4( )f x x
Absolute ValueTransformation Function
stretch (a) Stretch by a factor of 2
Compression (a) compressed by a factor of 14
reflection (a) Reflect over the x-axis
( )f x a x h k
( ) 2f x x1
4( )f x x
( )f x x
3( )f x x 3( )f x a x h k
CubicParent Function
Transformation Function
Horizontal Translation (h)
Move left 2 units
3( ) 2f x x
h moves left or right
3( ) 4f x x
Move right 4 units
3( )f x a x h k
Cubic
Transformation Function
vertical Translation (k)
Move down 3 units
3( ) 3f x x
k moves up or down
3( ) 5f x x
Move up 5 units
3( )f x a x h k Cubic
Transformation Function
stretch (a)
Stretch by a factor of 4
3( ) 4f x xCompression (a)
compressed by a factor of 1
8
31( )
8f x x
reflection (a)3( )f x x
Reflect over the x-axis
1( )f x
x
1( )f x a k
x h
Rational
Parent Function
Transformation Function
Horizontal Translation (h)
Move left 2 units h moves left or right
Move right 4 units
1( )
2f x
x
1
( )4
f xx
Rational
Transformation Function
vertical Translation (k)
Move up 3 units
1( ) 3f x
x
k moves up or down
Move down 5 units
1( )f x a k
x h
1( ) 5f x
x
RationalTransformation Function
stretch (a)
Stretch by a factor of 5
Compression (a)
compressed by a factor of
1
4
1( )f x a k
x h
1( ) 5f x
x 1 1
( )4
f xx
reflection1
( )f xx
(a)
Reflect over the x-axis
Rational1
( )f x a kx h
Transformation Function
