SOLUTION: Hi, Can someone please help me? . Can someone please explain how to find the 3 different kinds of asymptotes in a rational equation? ( Horizontal asymptotes, Vertical asymptotes,

Algebra ->  Rational-functions -> SOLUTION: Hi, Can someone please help me? . Can someone please explain how to find the 3 different kinds of asymptotes in a rational equation? ( Horizontal asymptotes, Vertical asymptotes,      Log On


   

Question 164998: Hi, Can someone please help me?
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Can someone please explain how to find the 3 different kinds of asymptotes in a rational equation? ( Horizontal asymptotes, Vertical asymptotes, Oblique asymptotes )
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Can you do sort of give a little lesson on this subject? ( Such things like, "How to find Horizontal, Vertical, Oblique asymptotes", " When can you have an Oblique asymptote", " How/When can you get "potholes"( points on a line that can't be in an equation ) ", and similar questions )
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Can you could give some rational equations ( several different kinds, ones that are fractions, improper fractions, ones that contain "potholes", and so forth ), along with how to find the asymptotes, or "potholes"
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Thank you so much ahead of time, Levi
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Vertical asymptote at x = 3: y = x/(x-3)
Horizontal asymptote at y = 1:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cx%2F%28x-3%29%29
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Horizontal asymptote at y = 3: y= 3x/(x-2)
Vertical asymptote at x=2
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C3x%2F%28x-2%29%29
------------------------------------
Oblique asymptote at y = x :y = (x^2 +x +2)/(x)
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28x%5E2%2Bx%2B2%29%2Fx%29
------------------
Pothole at x = 2:y = ((x-1)(x-2))/(x-2)
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28%28x-1%29%28x-2%29%29%2F%28x-2%29%29
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Cheers,
Stan H.