#### Answer

$y \text{ is NOT a function of }x
\\\text{Domain: }
(-\infty,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To determine if the given relation, $
x-y\lt3
,$ is a function, solve first for $y$ in terms of $x.$ Then check if $x$ is unique for every value of $y.$
To find the domain, find the set of all possible values of $x.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given relation is equivalent to
\begin{array}{l}\require{cancel}
x-y\lt3
\\\\
-y\lt-x+3
\\\\
-1(-y)\lt-1(-x+3)
\\\\
y\gt x-3
.\end{array}
If $x=0,$ then $y\gt-3.$ That is, the ordered pairs, $\{
(0,-2),(0,-1)
\}$ satisfy the given equation. This means that the value of $x$ is not unique. Hence, $y$ is NOT a function of $x.$
The variable $x$ can be replaced with any number. Hence, the domain is the set of all real numbers.
The given relation has the following characteristics:
\begin{array}{l}\require{cancel}
y \text{ is NOT a function of }x
\\\text{Domain: }
(-\infty,\infty)
.\end{array}