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Homework Help: Reciprocal of a function

  1. Mar 2, 2007 #1

    danago

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    Gold Member

    Given the following graph:
    http://img245.imageshack.us/img245/2395/scan0001ou4.gif [Broken]

    How can i sketch the reciprocal of that function? There are poles at x=-2 and x=2, so it means its reciprocal will have roots at -2 and 2 right? But thats not really enough information to compose a full sketch.

    How should i go about doing this?

    Thanks,
    Dan.
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 2, 2007 #2

    HallsofIvy

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    It's enough for a rough sketch. You can see that the function is symmetric about the y-axis so its reciprocal will be. You can see that at x= 0, the function has value just a little larger than -1 so its reciprocal will have value just a little less than -1. The reciprocal graph will start at x= 0, y= a little less than -1, rise to x= 2, y= 0, then continue increasing as x goes to + infinity. Use symmetry to get the graph for negative x.
     
  4. Mar 2, 2007 #3
    replace each y with 1/y for all x.
    eg. where y is tending to infinity, it should tend to 0.
     
  5. Mar 2, 2007 #4

    danago

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    So it will be similar to a quadratic graph?
     
  6. Mar 2, 2007 #5
    the middle portion is very similar to graph of -sec x, so its reciproca would be similar to -cos x
     
  7. Mar 2, 2007 #6
    1/big = small

    1/small = big
     
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