SOLUTION: If I have this function: g(x)=(8x)/(x^2+3x+4) how can I get the vertical & horizontal asymptotes?

Question 507488: If I have this function: g(x)=(8x)/(x^2+3x+4) how can I get the vertical & horizontal asymptotes?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If I have this function: g(x)=(8x)/(x^2+3x+4) how can I get the vertical & horizontal asymptotes?
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Vertical asymptotes occur when the denominator is zero.
Solve x^2+3x+4 = 0
Since b^2-4ac = 9-16 < 0,
there are no Real Number solutions.
So there are no vertical asymptotes.
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Horizontal asymptotes is the limit as x goes to +/-inf
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If you know something about calculus, divide numerator
and denominator by x^2 and take the limit:
y = limit as x goes to inf [(8/x)/(1 +3/x + 4/x^2)] = 0/1 = 0
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So horizontal asymptote at y = 0
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Cheers,
Stan H.
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