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Symmetry and Coordinate Graphs Section 3-1

Symmetry and Coordinate Graphs Section 3-1. How do we determine symmetry using algebra? How do we classify functions as even or odd?. Essential Questions:. Possible types of symmetry are:. with respect to the x -axis with respect to the y -axis with respect to the origin

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Symmetry and Coordinate Graphs Section 3-1

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  1. Symmetry and Coordinate GraphsSection 3-1 How do we determine symmetry using algebra? How do we classify functions as even or odd? Essential Questions:

  2. Possible types of symmetry are: • with respect to the x-axis • with respect to the y-axis • with respect to the origin • with respect to the line y = x • with respect to the liney = -x

  3. Table of Symmetric Relationships

  4. Equals original function x-axis What we do: keep x the same but negate y (1, 2) (1, -2)

  5. Equals original function y-axis What we do: keep y the same but negate x (1, 2) (-1, 2)

  6. Equals original function origin What we do: negate x AND negate y (-1, 3) (1, -3)

  7. Equals original function y = x interchange (swap) x and y What we do: (3, 2) (2, 3)

  8. Equals original function y = -x What we do: interchange AND negate x and y (2, 3) (-3, -2)

  9. x-axis y-axis origin y = x y = -x No No Yes Yes Yes Example 1 Determine the types of symmetry for the graph of xy = -2

  10. x-axis y-axis origin y = x y = -x yes yes yes no no Determine the types of symmetry for the graph of Example 2

  11. Classifying Functions as Even or Odd • EVEN functions are symmetric with respect to the y-axis • ODD functions are symmetric with respect to the origin

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