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#1 2006-01-02 11:59:56

Jacobpm
Guest

describing behavior on each side of a vertical asymptote

Find the vertical asymptotes of the graph of F(x) = (3 - x) / (x^2 - 16)

ok if i factor the denominator.. i find the vertical asymptotes to be x = 4, x = -4.

The 2nd part of the problem asks:
Describe the behavior of f(x) to the left and right of each vertical asymptote.. I'm not sure what i need to write for this.

#2 2006-01-02 15:08:23

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: describing behavior on each side of a vertical asymptote

When there is a vertical asymptote, either it approaches that asymptote going to infinity or negative infinity.  So pick a point just to the left of the asymptote, and see if it is positive or negative.  Then do it for the right (although you'll quickly learn you don't have to do it for both.  You'll see what I mean).

So find f(3.999), f(4.001), f(-3.999), and f(-4.001).

Last edited by Ricky (2006-01-02 15:08:54)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-01-02 15:09:34

darthradius
Member
Registered: 2005-11-28
Posts: 97

Re: describing behavior on each side of a vertical asymptote

I would guess that you need to say whether your function is going to positive or negative infinity on either side of the asymptotes...


The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
                                                             -Bertrand Russell

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#4 2006-01-02 15:11:19

darthradius
Member
Registered: 2005-11-28
Posts: 97

Re: describing behavior on each side of a vertical asymptote

whoops!...sorry, same time....


The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
                                                             -Bertrand Russell

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