CIE AS Maths: Pure 1

Revision Notes

1.5.1 Translations

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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, size, and orientation of the graph remain unchanged – the graph is merely shifted (up or down, left or right) in the xy plane

 

Translations What Is, A Level & AS Level Pure Maths Revision Notes

  • A particular translation (how far left/right, how far up/down) is specified by a translation vector: 

Translations Vector What Is, A Level & AS Level Pure Maths Revision Notes

 

What do I need to know about graph translations?

  • The graph of y equals straight f left parenthesis x right parenthesis plus a is a vertical translation of the graph y equals straight f left parenthesis x right parenthesis by the vector open parentheses table row 0 row a end table close parentheses
    • The graph moves up for positive values of and down for negative values of a
    • The x-coordinates stay the same

 

Translations statement_vert_Illustration, A Level & AS Level Pure Maths Revision Notes

  •  The graph of y equals straight f left parenthesis x plus a right parenthesis is a horizontal translation of the graph y equals straight f left parenthesis x right parenthesis by the vector open parentheses table row cell negative a end cell row 0 end table close parentheses
    • The graph moves left for positive values of and right for negative values of a
    • The y-coordinates stay the same

 Translations statement_horiz_Illustration, A Level & AS Level Pure Maths Revision Notes

  •  Any asymptotes of f(x) are also translated. If an asymptote is parallel to the direction of translation, however, it will not be affected

 Translations Asymptotes_Illustration, A Level & AS Level Pure Maths Revision Notes

Worked example

Translations Example, A Level & AS Level Pure Maths Revision Notes

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Roger

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Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.