Math  /  Calculus

QuestionDetermine the horizontal asymptote of the function. If none exists, state that fact. f(x)=2x34x+56x3+9x5f(x)=\frac{2 x^{3}-4 x+5}{6 x^{3}+9 x-5}
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, \square (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \square and the bottom asymptote is \square (Type equations.) C. The function has no horizontal asymptotes.

Studdy Solution
Find the leading coefficients:
The leading coefficient of the numerator is 2. The leading coefficient of the denominator is 6.
The horizontal asymptote is given by:
y=26=13 y = \frac{2}{6} = \frac{1}{3}
The function has one horizontal asymptote, y=13 y = \frac{1}{3} .

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