Question 92215: Find all (vertical and horizontal) asymptotes of f(x) = 2x^2 + 4x + 2 / 1-x^2. What is the domain of this function? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find all (vertical and horizontal) asymptotes of f(x) = 2x^2 + 4x + 2 / 1-x^2. What is the domain of this function?
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Factor where you can to get:
[2(x+1)^2]/[(1-x)(1+x)]
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Vertical asymptotes?
You have (x+1) in both numerator and denominator so you have a hole at x=-1
The denominator is zero when x=1 so you have a vertical asymptote at x=1.
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Horizontal asymptotes?
x^2 is the highest power and it appears in both numerator and denominator
The horizonal asymptote is the ratio of the coefficients of the hight power
term that appears in the rational expression:
y = 2/(-1) = -2
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Domain?
All Real Numbers except x=1 and x=-1
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Cheers,
Stan H.
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