Question 206879: find the horizontal and vertical asymptotes for the following functions if none type none f(x)=2x+3/x+2
g(x)=5x/x^2-1
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! f(x) = 3/(x+2)
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Vertical asymptote are zeros of denominator, (x+2)=0, x= -2
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Horizontal Asymptote is function of power on num / den, or n/m
in this case n less than m, therefore y=0
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g(x) = (5x)/(x^2 -1)
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Vertical asymptote is again zero of den,,(x^2-1)=0,,,x=+/- 1
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Hor Asymptote , n less than m, therefore y=0
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Rough sketch shows f(x) starts at - infinity approaching y=0 from bottom, steadily decreases as it approaches the asymptote at x=-2 at - infinity.
On the positive side of the x=-2 asymptote, function is at + infinity and steadily decreases to approach y=0 at + infinity
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.Rough sketch of g(x) shows three zones along x axis.
Starting at x= - infinity, the function is approaching y=0 from negative side, as function moves to right it decreases steadily to approach - infinity at x=-1. On the other side of the x=-1 asymptote, function is at - infinity, moves steadily upward to (0,0) then inverts the curve and steadily rises to + infinity at the x=1 asymptote. On the other side of x=1, function is at + infinity, dropping steadily to approach the y=0 asymptote at x= + infinity.
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Remember form of f(x) = a(n)x^(n) +...../b(m)x^m +....
when n less than m,,,,,y=o
when n=m,,,,,y=a/b
when n>m,,,,,,no asymptote
when n=(m+1),,,,slant asymptote
for HORIZONTAL Asymptotes
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