Question 444042: find the vertical and horizontal asymptote of the function: x+5/x^2+4x+8
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the vertical and horizontal asymptote of the function: x+5/x^2+4x+8
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If the degree of the numerator is less than the degree of the denominator, as in this case, the x-axis is the horizontal asymptote, that is, y=0
To find the vertical asymptotes, set the denominator=0, then solve for x.
x^2+4x+8=0
solve by quadratic formula:
a=1, b=4, c=8
x=[-4+-sqrt(4^2-4*1*8)]/2*1
x=(-4+-√-16)/2
This expression has two imaginary roots.
The denominator of the above expression can never be zero; for this reason, given function has no vertical asymptotes.
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