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← Odd Functions - College Algebra

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Showing Revision 4 created 08/07/2017 by Hajnalka Geib.

  1. If we try to fold any of the curves on
    this graph across the y-axis,
  2. none of them are going to
    map over to themselves.
  3. So, they must not have symmetry
    across the y-axis.
  4. The same is true of the x-axis
    when we try it there.
  5. Folding them in half along this line
    is not going to make points up here,
  6. match points down here, because they're on
    opposite sides of the y-axis.
  7. So, it looks like neither of these two
    symmetries applies
  8. in the case of odd functions.
  9. However, let's look at these last two
    choices, maybe one of them works.
  10. We know that this is a property of even
    functions, that points equidistant
  11. from the y-axis have the same y value,
  12. but it doesn't look like this is true
    of odd functions.
  13. If I pick some x coordinate like 5,
    and I find the given y coordinate,
  14. then finding the opposite
    x coordinate, negative 5
  15. does not give me the same y coordinate.
  16. It's all the way down here,
    instead of up here.
  17. However, these y coordinates are related.
  18. This one is the negative version
    of this one.
  19. So that means this last rule is true.