How can I sketch the reciprocal of a function with poles at x=-2 and x=2?

[danago]

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

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 that's not really enough information to compose a full sketch.

How should i go about doing this?

Thanks,
Dan.

 

[HallsofIvy]

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.

 

[f(x)]

replace each y with 1/y for all x.
eg. where y is tending to infinity, it should tend to 0.

 

[danago]

So it will be similar to a quadratic graph?

 

[f(x)]

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

 

[theperthvan]

1/big = small

1/small = big