Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 402: 133


The provided statement is true.

Work Step by Step

For a rational function, say $F\left( x \right)=\frac{P\left( x \right)}{Q\left( x \right)}$ , the vertical asymptote depends on the denominator term. Equate $Q\left( x \right)$ to 0, and calculate asymptotes based on the values of x obtained. At the points where $Q\left( x \right)=0$ the rational function is not defined and hence a vertical asymptote can never cross the graph of the function. Also, an asymptote is defined as a line which a function approaches, but never meets. Hence, a rational function cannot ever cross the asymptote. Therefore, the given statement is true.
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