Look at the following two curves. The minimum distance between the curves is decreasing and this is what gives us the impression that the two curves are converging. If the important information is the vertical distance between curves or between a curve and set of points, graph the vertical distance explicitly, even if it requires another graph. Good, informative graphs are hard to construct. You have to balance the level of decoding with questions of distance and detection.
Good graphics is an art as much as it is a science.