I am not familiar with the a graph that looks to be a function within a function.

I have a graph that looks to be asine curve, but the ending points look to be travelling towards a distinct point. If u take a slope of the tangants on this area of this curve, the slope seems to reach an infinity/undefined slope.

Is there a way I can prove this to be a function within a function? I know there is a certain curve that has these similar propoertties, in which there is a 1 period of a sine curve, whose ending points are connected by downward sloping line segments.

But how would I prove any graph to be a function within a function, especially a trigonometric function within a function.

Thanks!