Answer
$\text{(a)}$ function; domain is $\{2,4,6,8 \}$ and range is $\{5,6,7,8 \}$
$\text{(b)}$ not a function.
$\text{(c)}$ not a function
$\text{(d)}$ function; domain is $(-\infty,\infty)$ and range is $[2,\infty)$
Work Step by Step
$\text{(a)}$ As each $x$ corresponds to only one $y$, it is a function with domain $\{2,4,6,8 \}$ and range $\{5,6,7,8 \}$
$\text{(b)}$ $x=1$ corresponds to the $y$ values $3$ and $7$ thus the relation is not a function.
$\text{(c)}$ When a vertical line test is performed, the given relation will fail it because vertical lines such as $x=0$ will pass through more than one point on the graph. Thus, the given graph does not represent a function.
$\text{(d)}$ The given graph will pass the vertical line test since every vertical line will pass through only one point on the curve. Thus, the given graph represents a function.
The graph shows that $x$ can be any real number so the domain $is (-\infty,\infty)$.
The value of $y$ is $2$ or higher so the range $[2,\infty)$
