Question 429773
 How do I find out what the Vertical Asymptote is for this function:
2x^2-6/x^3-8? 

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Factor:
[2(x^2-6)]/[(x-2)(x^2+2x+4)]
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You have a vertical asymptote when the denominator 
of this problem is zero.
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Solve x^2+2x+4 = 0
x = [-4+-sqrt(4-4*4)]/2
Solution is imaginary since the discriminant is negative.

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Vertical asymptote at x = 2 only. 
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{{{graph(400,300,-10,10,-10,10,(2x^2-6)/(x^3-8))}}}
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Cheers,
Stan H.