# Reciprocal of a function

1. Mar 2, 2007

### danago

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. Mar 2, 2007

### HallsofIvy

Staff Emeritus
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. Mar 2, 2007

### f(x)

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

4. Mar 2, 2007

### danago

So it will be similar to a quadratic graph?

5. Mar 2, 2007

### f(x)

the middle portion is very similar to graph of -sec x, so its reciproca would be similar to -cos x

6. Mar 2, 2007

### theperthvan

1/big = small

1/small = big