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: 19

Answer

The given relation does not represent $y$ as a function of $x$. domain: $[-6, 6]$ range: $[-6, 6]$

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 a number of vertical lines (e.g., $x=0$) will pass through the 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 x-values vary from $-6$ to $6$ so the domain is $[-6, 6]$. The y-values vary from $-6$ to $6$ so the range is $[-6, 6]$.
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