Yes this is a function
The reason why is because the x coordinates do not repeat. Each x value maps to exactly one y value. For any input, there is exactly one output. If you were to graph all of these points, then the graph would pass the vertical line test.
If we had something like (2,4) and (2,0) then the input x = 2 would lead to multiple outputs (y = 4, y = 0) which would not make it a function; however we don't have any repeated x values here.