Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.6 - Rational Expressions - 3.6 Exercises - Page 309: 34

Answer

Vertical asymptotes: $x=1$ and $x=-1$ Horizontal asymptote: $y=0$

Work Step by Step

$r(x)=\dfrac{3x^{2}+5x}{x^{4}-1}$ Vertical asymptotes A rational function has vertical asymptotes where the function is undefined, that is, where the denominator is zero. Set the denominator equal to $0$ and solve for $x$ to find the vertical asymptotes of this function: $x^{4}-1=0$ $x^{4}=1$ $\sqrt[4]{x^{4}}=\sqrt[4]{1}$ $x=\pm1$ Horizontal asymptote Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote of this function is $y=0$
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