Question

State the horizontal asymptote of the rational function. For full credit, explain the reasoning you used to find the horizontal asymptote. F(x) =quantity x plus nine divided by quantity x squared plus four x plus two

Answer 1

Answer:

y=0

Step-by-step explanation:

Answer 2

F(x) = $\frac{x + 9}{x^{2} + 4x + 2}$

For horizontal asymptote, evaluate only the term of the numerator (top) and denominator (bottom) that has the greatest exponent.  F(x) = $\frac{x}{x^{2}}$.

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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 = $\frac{coefficient (of numerator)}{coefficient (of denominator)}$

If n < m, then asymptote is: y = $\frac{1}{infinity}$, so y = 0

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F(x) = $\frac{x}{x^{2}}$   ⇒   y = $\frac{1}{infinity}$  ⇒  y = 0

Answer: y = 0