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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.

Previous:Graphing InequalitiesNext:Sequences

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation