Look at the y axis. You can see that the graph reaches a minimum at y=3, and then grows indefinitely.
This implies that the range is [tex][3,\infty)[/tex]. In fact, the range is exactly the set of all values reached by the function's outputs.
The vertical line test states that a graph is a function if and only if every possible vertical line crosses the graph at most once.
You can see that this is the case, so this is the graph of a function indeed.