Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises: 21

Answer

The given relation does not represent $y$ as a function of $x$. domain: $(-\infty, +\infty)$ range: $(-\infty, -1] \cup [1, +\infty)$

Work Step by Step

RECALL: Vertical Line Test If all vertical lines will pass through the graph of a relation in at most one point only, then the relation defines $y$ as a function of $x$. To know if the given graph represents $y$ as a function of $x$, perform the vertical line test. Note that vertical lines $x=3$ will pass through the given graph at two points. This means that the graph fails the vertical line test. Thus, the given relation does not represent $y$ as a function of $x$. The graph covers all x-values so the domain is $(-\infty, +\infty)$. The graph covers y-values that are either greater than or equal to $1$ or less than or equal to $-1$. Thus, the range is $(-\infty, -1] \cup [1, +\infty)$.
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