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AS Maths CIE Your notes
1.5 Transformations of Functions
Contents
1.5.1 Translations
1.5.2 Stretches
1.5.3 Reflections
Page 1 of 32
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1.5.1 Translations
Your notes
Translations
What are graph transformations?
When you alter a function in certain ways, the effects on the graph of the function can be
described by geometrical transformations
With a translation the shape, siz e, and orientation of the graph remain unchanged – the graph is
merely shifted (up or down, left or right) in the xy plane
A particular translation (how far left/right, how far up/down) is specified by a translation vector:
Page 2 of 32
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Your notes
What do I need to know about graph translations?
⎛⎜ 0 ⎞⎟
The graph of y = f (x ) + a is a vertical translation of the graph y = f (x ) by the vector ⎜⎜ ⎟⎟
⎝a ⎠
The graph moves up for positive values of a and down for negative values of a
The x-coordinates stay the same
Page 3 of 32
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Your notes
Page 4 of 32
© 2015-2023 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers
AS Maths CIE Your notes
1.5 Transformations of Functions
Contents
1.5.1 Translations
1.5.2 Stretches
1.5.3 Reflections
Page 1 of 32
© 2015-2023 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers
, Head to savemyexams.com for more awesome resources
1.5.1 Translations
Your notes
Translations
What are graph transformations?
When you alter a function in certain ways, the effects on the graph of the function can be
described by geometrical transformations
With a translation the shape, siz e, and orientation of the graph remain unchanged – the graph is
merely shifted (up or down, left or right) in the xy plane
A particular translation (how far left/right, how far up/down) is specified by a translation vector:
Page 2 of 32
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Your notes
What do I need to know about graph translations?
⎛⎜ 0 ⎞⎟
The graph of y = f (x ) + a is a vertical translation of the graph y = f (x ) by the vector ⎜⎜ ⎟⎟
⎝a ⎠
The graph moves up for positive values of a and down for negative values of a
The x-coordinates stay the same
Page 3 of 32
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Your notes
Page 4 of 32
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