A function is only possible if any x input leads to exactly one y output. For choices B, C and D, we see that the graphs fail the vertical line test. It is possible to draw a single vertical line through more than one point on the curve. So for these graphs, we have x inputs lead to multiple outputs, and that makes them not a function.
Choice A shows the graph passing the vertical line test. It is not possible to draw a single vertical line through more than one point on the diagonal line. Therefore this graph is a function.
