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 - Page 297: 20


The given relation does not represent $y$ as a function of $x$. domain: $(-\infty, +\infty)$ range: $[0, +\infty)$

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 the vertical line $x=3$ passes through the given graph at an infinite number of 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 y-values are greater than or equal to zero so the range is $[0, +\infty)$.
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