SOLUTION: What is horizontal asymptote and vertical asymptote of g(x)=5x/x^2-1? Thank you.

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Question 206973: What is horizontal asymptote and vertical asymptote of g(x)=5x/x^2-1? Thank you.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29+=+5x%2F%28x%5E2-1%29
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if x = +/- 1 then x^2-1 = 0 so you will get a vertical asymptote at that point.
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the vertical asymptote is when x approaches infinity but never quite reaches it ---
the horizontal asymptote would be the value of y when x approaches infinity.
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a good treatment of this subject can be found at:
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http://www.purplemath.com/modules/asymptote.htm
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a graph of your equation to show the vertical asymptotes is as follows:
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graph+%28400%2C400%2C-3%2C3%2C-10%2C10%2C5x%2F%28x%5E2-1%29%29
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it appears that the horizontal asymptote is equal to 0 because as x approaches infinity, y approaches 0.
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a graph of your equatrion to show the horizontal asymptotes is as follows:
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graph+%28800%2C400%2C-40%2C40%2C-4%2C4%2C5x%2F%28x%5E2-1%29%29
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there is lots more information at the website i recommended so check it out if you need to know more.
they also treat slanted asymptotes.
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vertical asymptotes never cross the vertical line they approach.
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horizontal asymptote can cross the horizontal line they approach.
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enjoy