All three of those graphs are functions.
The main thing about a function is for every input in the domain there is exactly one output. That doesn't mean that there has to be a y for every x; the xs with no output, no y, are not in the domain of the function.
So to be a function for every x there needs to be <em>at most one </em>y.
The test for that is called the <em>vertical line test.</em> If you can draw a vertical line (x=constant) through two points of the graph, that graph does not represent a function.
All three of these functions pass the vertical line test. For the first the questionable point is x=-2. A vertical line there passes through the graph at y=0. It doesn't pass through the graph at y=-2 -- the open circle means that interval is open, it doesn't include (-2,-2). So a vertical line passes through at most one point on the graph at all (shown) places, therefore it's a function.
The second one is similar at x=-2. At x=0 there's an open point; the function has no value there. x=0 is not part of the domain. That doesn't mean this isn't a function; it passes the vertical line test, so it's a function.
The third is like the second except now at x=-2 the value's in the right branch, y=-8. Still this passes the vertical line test, so it's a function too.
Answer: all of the above
