## Intermediate Algebra (12th Edition)

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