SOLUTION: Find the horizontal and vertical asymptotes for the following rational function f(x) = (x^2 + 2x + 5) / (3x^2 - 11)

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Question 477515: Find the horizontal and vertical asymptotes for the following rational function
f(x) = (x^2 + 2x + 5) / (3x^2 - 11)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the horizontal and vertical asymptotes for the following rational function
f(x) = (x^2 + 2x + 5) / (3x^2 - 11)
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When the degree of the numerator and denominator are the same, as in this case, divide the lead coefficient of the the numerator by the lead coefficient of the denominator. The resulting quotient is the horizontal asymptote.
Horizontal asymptote: y=1/3
..
To find the vertical asymptotes, set the denominator=0, then solve for x.
3x^2-11=0
3x^2=11
x^2=11/3
x=±√(11/3)
Vertical asymptotes:
x=√(11/3)
and
x=-√(11/3)