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: 41

Answer

The given relation defines $y$ as a function of $x$. domain: $(-\infty, +\infty)$ range: $[0, +\infty)$

Work Step by Step

RECALL: A function is a relation where every value of $x$ is paired with only one $y$ value. The give equation will given only one value of $y$ for every value of $x$. This means that each $x$ is paired with only one value of $y$. Thus, the given relation defines $y$ as a function of $x$. Negative numbers have no real number square roots. Thus, the value of $x$ cannot be negative. This means that the domain of the given function is the set of all non-negative real numbers. In interval notation, the domain is $(-\infty, +\infty)$. The principal square of a number is always 0 or higher. Thus, the value of $y$ is always greater than or equal to zero. In interval notation, the range is $[0, +\infty)$.
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