Answer
$y \text{ is a function of }x
\\\text{Domain: }
\left[ -\dfrac{9}{2},\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}