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Write an equation of the slant or nonlinear asymptote. \[ r(x)=\frac{-x^{3}-13 x^{2}-35 x+3}{x+9} \] The (Choose one) \( \nabla \) asymptote is \( y=\square \)

Ask by Burns Tran. in the United States
Mar 18,2025

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The slant asymptote is \( y = -x^2 - 4x + 1 \).

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To find the slant asymptote of the rational function \( r(x) = \frac{-x^3 - 13x^2 - 35x + 3}{x + 9} \), you need to perform polynomial long division. When you divide \( -x^3 - 13x^2 - 35x + 3 \) by \( x + 9 \), you'll find that the quotient gives you the linear equation for the asymptote, while the remainder can be ignored for large values of \( x \). Upon dividing, you'll find that the slant asymptote is: \( y = -x^2 - 4x + 3 \). Thus, the slant asymptote is \( y = -x^2 - 4x + 3 \).

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