## Intermediate Algebra (12th Edition)

$y \text{ is a function of }x \\\text{Domain: } \left[ -\dfrac{9}{2},\infty \right)$
$\bf{\text{Solution Outline:}}$ To determine if the given equation, $y=\sqrt{2x+9} ,$ 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 $x.$ $\bf{\text{Solution Details:}}$ For each value of $x,$ multiplying it by $2$ and then adding $9$ will produce a single value of $y.$ Hence, $y$ is a function of $x.$ The radicand, $2x+9,$ of a radical with an even index cannot be negative. Hence, \begin{array}{l}\require{cancel} 2x+9\ge0 \\\\ 2x\ge-9 \\\\ \dfrac{2x}{2}\ge-\dfrac{9}{2} \\\\ x\ge-\dfrac{9}{2} .\end{array} The given equation has the following characteristics: \begin{array}{l}\require{cancel} y \text{ is a function of }x \\\text{Domain: } \left[ -\dfrac{9}{2},\infty \right) .\end{array}