Precalculus (6th Edition)

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

Chapter 2 - Graphs and Functions - 2.3 Functions - 2.3 Exercises - Page 215: 31


The given relation defines a function. domain: $(-\infty, +\infty)$ range: $(-\infty, +\infty)$

Work Step by Step

Note that all vertical lines will pass through the graph in at most one point. This means that the graph pass the vertical line test. Thus, the given graph represents a function. The graph covers all real numbers from left to right so the function is defined for all values of $x$. This means the domain is $(-\infty, +\infty)$. The graph covers all real numbers from bottom to top so value of $y$ can be any real number. This means the range is $(-\infty, +\infty)$.
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