Answer
$y \text{ is a function of }x
\\\text{Domain: }
\left( -\infty,\infty \right)
\\\text{NOT a linear function}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
