When trying to determine if a graph is a function, you can use the vertical line test: Pass a vertical line from left-to-right across the graph. If it touches the graph is more than one location, it is not a function. Otherwise, it is.
Let's take a look at your graph with the vertical line test:
Notice that we are able to touch the graph in two different locations when x=2.
That means this function is NOT a vertical line.
Specifically for the answer choices you've given, the correct answer is B: The vertical line test fails when x > 0.