SOLUTION: Please can someone help me understand end behavior on a graph?? also how to graph this function showing horizontal and vertical asymptotes: R(x)= 2(x-1/2)(x+1)/(x+2)(x-1)

Algebra ->  Rational-functions -> SOLUTION: Please can someone help me understand end behavior on a graph?? also how to graph this function showing horizontal and vertical asymptotes: R(x)= 2(x-1/2)(x+1)/(x+2)(x-1)       Log On


   

Question 571994: Please can someone help me understand end behavior on a graph??
also how to graph this function showing horizontal and vertical
asymptotes: R(x)= 2(x-1/2)(x+1)/(x+2)(x-1)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
also how to graph this function showing horizontal and vertical
asymptotes: R(x)= 2(x-1/2)(x+1)/(x+2)(x-1)
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Horizontal Asymptote:
For polynomial expressions the following works:
End behavior = highest power term / highest power term
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y = (2x^2)/(x^2) = 2
y = 2 is the horizontal asymptote
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Vertical Asymptotes:
x = -2 and x = 1 because both values cause the denominator to go to zero.
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End behavior is determined by the horizontal asymptote.
y goes to 2 as x goes to + and to - infinity.
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Cheers,
Stan H.