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: 41

Answer

Vertical asymptote: $x=1$ Horizontal asymptote: None

Work Step by Step

$t(x)=\dfrac{x^{2}+2}{x-1}$ Vertical asymptote 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: $x-1=0$ $x=1$ Horizontal asymptote: The degree of the numerator is greater than the degree of the denominator. This function has no horizontal asymptote.
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