Yes, the graph represents a function, because each x-value has exactly one corresponding y-value. This is the definition of a function. So the answer is C.
You can see this by drawing a vertical line anywhere across the graph. The line will only intersect the graph once for any given x-value.
The other answer choices are incorrect because:
A is incorrect because there are no y-values in the graph that are paired with two x-values.
B is incorrect because the graph does not need to touch the y-axis exactly once to be a function.
D is incorrect because closed circles are not required to show where a graph ends. The graph can end at any point on the coordinate plane.