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 216: 39


The given relation does not define $y$ as a value of $x$. domain: $(-\infty, +\infty)$ range : $(-\infty, +\infty)$

Work Step by Step

RECALL: A function is a relation where every value of $x$ is paired with only one $y$ value. Substituting $0$ to $x$ gives: $x+y \lt 3 \\0+y \lt 3 \\y \lt 3$. This means when $x=0$, $y$ can be any real number less than $3$. Thus, when $x=0$, the points $(0, 2), (0, 1), (0, 0)$, plus a lot of others satisfy the inequality. An $x$ value is paired with more than one value of $y$, then the given relation does not define $y$ as a value of $x$. $x$ and $y$ can take any value therefore: domain: $(-\infty, +\infty)$ range : $(-\infty, +\infty)$
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