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GCSEMathsEdexcelHigherFlashcards2. AlgebraTransformations of Graphs

Transformations of Graphs (Edexcel GCSE Maths)

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  • FrontTranslations of Graphs

    True or False?

    Translating a graph maintains its shape, size, and orientation.

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Cards in this collection (13)

  • True or False?

    Translating a graph maintains its shape, size, and orientation.

    True.

    Translating a graph maintains its shape, size, and orientation.

    It only moves the graph up/down/left/right.

  • When a graph is translated by the vector open parentheses table row a row b end table close parentheses, how many units does it move and in which direction(s)?

    When a graph is translated by the vector open parentheses table row a row b end table close parentheses, it moves a units right and b units upwards.

    If a is negative then it moves left, and if b is negative it moves downwards.

  • A graph is transformed from straight f open parentheses x close parentheses to straight f open parentheses x minus a close parentheses. Describe the transformation fully.

    If a graph is transformed from straight f open parentheses x close parentheses to straight f open parentheses x minus a close parentheses, this is a translation of a units right.

  • A graph is transformed from straight f open parentheses x close parentheses to straight f open parentheses x close parentheses plus b. Describe the transformation fully.

    If a graph is transformed from straight f open parentheses x close parentheses to straight f open parentheses x close parentheses plus b, it has been translated vertically upwards by b units.

  • True or False?

    When a graph is translated, any asymptotes remain in the same location(s).

    False.

    When a graph is translated, any asymptotes are also translated in the same way as the rest of the graph.

  • Outline how would you find a new equation for a graph which has been translated horizontally.

    To find a new equation for a graph which has been translated horizontally, consider how the function has been changed.

    It has changed from straight f open parentheses x close parentheses to straight f open parentheses x minus a close parentheses, this is a translation of a units right.

    Therefore in the equation of the graph, you can simply replace x with open parentheses x minus a close parentheses.

    E.g. y equals x squared becomes y equals open parentheses x minus a close parentheses squared.

  • Outline how would you find a new equation for a graph which has been translated vertically.

    To find a new equation for a graph which has been translated vertically, consider how the function has been changed.

    It has changed from straight f open parentheses x close parentheses to straight f open parentheses x close parentheses plus a, this is a translation of a units upwards.

    Therefore in the equation of the graph, you can simply add on a

    E.g. y equals x squared becomes y equals x squared plus a.

  • Describe the transformation that has occurred when y equals x squared is transformed to open parentheses x minus p close parentheses squared plus q.

    When y equals x squared is transformed to open parentheses x minus p close parentheses squared plus q, it has been translated p units right, and q units upwards.

    This is why when completing the square, the vertex is at open parentheses p comma space q close parentheses.

  • The graph of y equals straight f open parentheses x close parentheses is transformed to y equals negative straight f open parentheses x close parentheses.

    Describe the transformation that has occurred.

    When the graph of y equals straight f open parentheses x close parentheses is transformed to y equals negative straight f open parentheses x close parentheses, the graph has been reflected in the x-axis.

  • The graph of y equals straight f open parentheses x close parentheses is transformed to y equals straight f open parentheses negative x close parentheses.

    Describe the transformation that has occurred.

    When the graph of y equals straight f open parentheses x close parentheses is transformed to y equals straight f open parentheses negative x close parentheses, the graph has been reflected in the y-axis.

  • True or False?

    Some graphs appear not to change when reflected.

    True.

    Some graphs appear not to change when reflected.

    E.g. y equals x squared will look exactly the same when reflected in the y-axis.

  • Outline how would you find a new equation for a graph which has been reflected in the x-axis.

    To find a new equation for a graph which has been reflected in the x-axis, consider how the function has been changed.

    It has changed from straight f open parentheses x close parentheses to negative straight f open parentheses x close parentheses.

    Therefore you multiply the whole equation of the graph by -1.

    E.g. y equals x squared minus 7 x plus 10 becomes y equals negative open parentheses x squared minus 7 x plus 10 close parentheses or y equals negative x squared plus 7 x minus 10.

  • Outline how would you find a new equation for a graph which has been reflected in the y-axis.

    To find a new equation for a graph which has been reflected in the y-axis, consider how the function has been changed.

    It has changed from straight f open parentheses x close parentheses to straight f open parentheses negative x close parentheses.

    Therefore you replace all the x's with negative x.

    E.g. y equals x squared minus 7 x plus 10 becomes y equals open parentheses negative x close parentheses squared minus 7 open parentheses negative x close parentheses plus 10 or y equals x squared plus 7 x plus 10.

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