F(x) = [tex]\frac{x + 9}{x^{2} + 4x + 2}[/tex]
For horizontal asymptote, evaluate only the term of the numerator (top) and denominator (bottom) that has the greatest exponent. F(x) = [tex]\frac{x}{x^{2}}[/tex].
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If n > m, the asymptote is: y = ∞, so asymptote does not exist
If n = m, then the asymptote is the ratio of the coefficients: y = [tex]\frac{coefficient (of numerator)}{coefficient (of denominator)}[/tex]
If n < m, then asymptote is: y = [tex]\frac{1}{infinity}[/tex], so y = 0
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F(x) = [tex]\frac{x}{x^{2}}[/tex] ⇒ y = [tex]\frac{1}{infinity}[/tex] ⇒ y = 0
Answer: y = 0
