Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.5 - Introduction to Relations and Functions - 2.5 Exercises - Page 195: 48


$y \text{ is a function of }x \\\text{Domain: } (-\infty,\infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To determine if the given equation, $ y=6x+8 ,$ is a function, check if every value of $x$ will produce a different value of $y.$ To find the domain, find the set of all possible values of $x.$ $\bf{\text{Solution Details:}}$ For each value of $x,$ multiplying it by $ 6 $ and then adding $8$ will produce a different value of $y.$ Hence, $y$ is a function of $x.$ The variable $x$ can be replaced with any number. Hence, the domain is the set of all real numbers. Hence, the given equation has the following characteristics: \begin{array}{l}\require{cancel} y \text{ is a function of }x \\\text{Domain: } (-\infty,\infty) .\end{array}
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