## Intermediate Algebra (12th Edition)

$y \text{ is a function of }x \\\text{Domain: } \left( -\infty,\infty \right) \\\text{NOT a linear function}$
$\bf{\text{Solution Outline:}}$ To determine if the given equation, $y=|x| ,$ is a function, check if $x$ is unique for every value of $y.$ To find the domain, find the set of all possible values of $x.$ A linear function is any equation that can be expressed as $f(x)=mx+b.$ $\bf{\text{Solution Details:}}$ For any $x,$ taking the absolute value will produce only $1$ value of $y.$ Hence, $y$ is a function of $x.$ The variable $x$ can take any value. Hence, the domain is the set of all real numbers. Since the given equation cannot be expressed as $f(x)=mx+b,$ then it is not a linear function. The given equation has the following characteristics: \begin{array}{l}\require{cancel} y \text{ is a function of }x \\\text{Domain: } \left( -\infty,\infty \right) \\\text{NOT a linear function} .\end{array}