Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Concept and Vocabulary Check - Page 398: 9

Answer

Based on the synthetic division shown below, the equation of the slant asymptote of $f\left( x \right)=\frac{3{{x}^{2}}-7x+5}{x-4}$ is $y=3x+5$.

Work Step by Step

Divide $3{{x}^{2}}-7x+5$ by $x-4$. Use synthetic division, $\begin{align} & \left. {\underline {\, 4 \,}}\! \right| \ 3\ -7\ 5 \\ & \ \ \underline{\ \ \ \ 12\ 20} \\ & \ \ 3\ \ \ 5\ \ 25 \\ \end{align}$ The reminder is 25. So, $f\left( x \right)=3x+5+\frac{25}{x-4}.$ The equation of the asymptote is $y=3x+5$.
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