You can put this solution on YOUR website! Vertical asymptotes result from a function not being defined. The only thing to worry about here is the denominator. We cannot divide by 0. So x^2+4 cannot = 0. This will never happen because x^2+4>=4>0 for all real x.
Now, horizontal asymptotes result from the limitations implemented by numerator and denominator. Since this rational function has D(n)>D(d) (degree of numerator greater than degree of denominator), we will have a slant asymptote. We find such an asymptote by performing division and leaving out the remainder.
......x
x^2+4)x^3+0x^2+0x+8
....-(x^3+4x)
_____________
........-4x+8
So y=x is the slant asymptote.
Graph:
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