The most important aspect to have into account for a graph to be a function is that the function has a domain, and this domain has only an image in the range.
If we pass a vertical line through the function, we can check that the line will pass through this graph in only one point.
In this way, we can say that for each element of the domain, we have only one element in the range. Then, graphically, we have:
Therefore, we can say that this graph is a function.