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

y=0

Explanation:

Answer 2

F(x) =
`(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) =
`(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 =
`(coefficient (of numerator))/(coefficient (of denominator))`

If n < m, then asymptote is: y =
`(1)/(infinity)`, so y = 0

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F(x) =
`(x)/(x^(2))` ⇒ y =
`(1)/(infinity)` ⇒ y = 0

Answer: y = 0