Answer
Function.
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,4$]
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 no more than one point, indicating that there is only one $y$ value for each $x$ value.
We can see that the domain is all real numbers and the range is all values less than or equal to $4$:
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,4$]