Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 8 - Rational Functions - 8-4 Rational Expressions - Practice and Problem-Solving Exercises - Page 533: 54

Answer

There are no vertical asymptotes for this function. There is a hole at $x = 3$ on the graph.

Work Step by Step

To find the vertical asymptote, find the zeros of the denominator by setting each factor equal to zero and solving: $x - 3 = 0$ $x = 3$ We have a vertical asymptote at $x = 3$ only if it is not a zero of the numerator. In this exercise, $x = 3$ is also a zero of the numerator; therefore, it is not a vertical asymptote of this function. This also means that $x = 3$ is a removable discontinuity or hole that can be removed by filling in a single point.
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