Answer
Function.
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,\infty)$
Work Step by Step
This graph is a function because it passes the vertical line test -- an arbitrary vertical line will only pass the graph at one point, indicating that there is only one $y$ value for each $x$ value.
We can see that both the domain and range consist of all real numbers (the graph spans all values of x and y).:
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,\infty)$