College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.2 - Properties of Rational Functions - 5.2 Assess Your Understanding - Page 352: 50

Answer

The only vertical asymptote is x=1. The only horizontal asymptote is y=0. There are no oblique asymptotes.

Work Step by Step

To find asymptotes, first, we must make sure the function is in the lowest terms. To find vertical asymptotes, we must find the values that make the denominator equal zero. In this case: $x^3-1=0$ $x^3=1$ $\sqrt[3]{x^3}=\sqrt[3]1$ $x=1$ There are two cases to determine horizontal asymptotes. If the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote will be y = 0. If the degrees of both the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients. In this case, we can see that the degree of the denominator is greater than the one in the denominator, so the horizontal asymptote is y=0. To determine oblique asymptotes, the degree of the numerator must be one degree greater than the degree of the denominator. Since that requirement is not being met here, there are no oblique asymptotes.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.