Answer
$y \text{ is NOT a function of }x
\\\text{Domain: }
\left( -\infty,\infty \right)
\\\text{NOT a linear function}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To determine if the given inequality, $
y\lt x+2
,$ 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 where the highest exponent of all the variables is $1.$
$\bf{\text{Solution Details:}}$
If $x=0,$ then
\begin{array}{l}\require{cancel}
y\lt 0+2
\\\\
y\lt 2
.\end{array}
Hence, the ordered pairs, $\{ (0,0),(0,1) \}$ satisfy the given inequality. Since $x$ is not unique, then the given inequality is not a function.
The variable $x$ can take any value. Hence, the domain is the set of all real numbers.
Since the inequality is not a function, then the given does not define a linear function.
The given inequality has the following characteristics:
\begin{array}{l}\require{cancel}
y \text{ is NOT a function of }x
\\\text{Domain: }
\left( -\infty,\infty \right)
\\\text{NOT a linear function}
.\end{array}
