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← Which is Which - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. So, we still have x squared and x cubed functions graphed over here on this
  2. coordinate plane. And here, I have y equals x to the 4th graphed as well. I'd
  3. like you to take a second and compare the overall behavior of x to the 4th to x
  4. squared. I know that all three of these graphs actually go through the origin.
  5. Which makes sense, because zero taken to any power is just equal to zero. So we
  6. plug in zero for x, and any of them, the y value is going to be zero as well.
  7. However, both of the graphs that have even powers have that property that I
  8. talked about in the previous answer video. Either end of the graph is going to
  9. point in the same direction. Either going to have a sort of U-shape overall or
  10. sort of upside down U-shape. The U for x to the 4th just happens to be a bit
  11. steeper than it does for x squared. So, let's see if this pattern continues as
  12. we move even higher in degree with our polynomial functions. Yet again, I've
  13. added more graphs. One of these is the graph of y equals x to the 5th, and one
  14. of them is the graph of y equals x to the 6th. So, thinking about the patterns
  15. that you noticed over here with our first three graphs that you're considering,
  16. what do you think the overall behavior of this 5th degree function will look
  17. like versus the 6th degree function?