College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.5 - Page 407: 27


Vertical asymptotes: none Holes: none

Work Step by Step

Locating Vertical Asymptotes, (page 395) tells us that for $f(x)=\displaystyle \frac{p(x)}{q(x)}$, if p(x) and q(x) have NO common factors, and a is a zero of the denominator $q(x)$ , then the line $x=a$ is a vertical asymptote. BUT, if they DO have common factors, after REDUCING the form of the function's equation, the number a may not cause the denominator to be zero any more. in which case there will be a hole at x=a. The point is that both p(x) and q(x) have to be factored, and if we can, then we reduce the expression for f(x). ------------------ $r(x)=\displaystyle \frac{x}{x^{2}+4}$ $p(x)=x\qquad $... fully factored $q(x)=x^{2}+4\qquad $... fully factored Nothing to reduce.... $q(x)=0$ $x^{2}+4=0$ $x^{2}=-4$ ... no real number has a negative square. Since the denominator , q(x) has no zeros r is defined for all real numbers, meaning Vertical asymptotes: none Holes: none
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.