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Aims:• To interpret and apply
transformations of functions:
• To know the effects of combinations of transformations and represent the results graphically and algebraically
DCBxAf )(
DCBxAf )(
Y are we stuck outside the function?
We are inside the function - Xactly where we want to be!
3x
f(x) f(3x+12)
Replace x with 3x
f ( )x
Replace x with x+4
(x+4)f( 3 )x =f(3x+12)
OR
x+12
Replace x with x+12
f ( )x
Replace x with 3x
3xf( +12)x
The aim is to change this
into this, by using 2 single step transformations
There are 2 methods shown here:
Transformation Situation
• Your task is to identify which two shapes’ transformations give rise to the desired transformation.
• E.g.
5x-3 15(x-3)-9
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
f(x)=x3+x 3(x-3)3+3(x-3)
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
2x 2/3x+3
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
x2 1/9x2+3
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
sinx 3sin(1/3x)
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
ex ex-3+3
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
f(x) f(1/3x)+3
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in y
x2 x2-6x+12
Translation 3 units in y direction
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
f(x) 3f(1/3x)
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
x 1/3x-1Translation 3 units in x direction
Stretch sf 3 in x
Translation 3 units in x direction
Stretch sf 3 in
x
Stretch sf 3 in yTranslation 3 units in y direction
x 1/3x-3Translation 3 units in x direction
Stretch sf 3 in x
Phew
• But hang on…Which pair of transformations would
change…(hint one is a reflection)f(x)=x2 into 4x-x2-4?
Thank heavens there were no
reflections!
