Reciprocal of a function

  • Thread starter danago
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  • #1
danago
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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.
 
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  • #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.
 
  • #3
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replace each y with 1/y for all x.
eg. where y is tending to infinity, it should tend to 0.
 
  • #4
danago
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So it will be similar to a quadratic graph?
 
  • #5
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So it will be similar to a quadratic graph?
the middle portion is very similar to graph of -sec x, so its reciproca would be similar to -cos x
 
  • #6
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1/big = small

1/small = big
 

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