Question

PLZ HELP!!! Which graph represents the function?

Answer 1

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 at most one y.

The test for that is called the vertical line test.  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