Reflecting inverse graphs

An inverse exchanges the input and output of every permitted pair: (a,b) to (b,a). Thus its graph is a reflection in y=x, using equal coordinate scales. Swap intercepts and endpoints, retaining whether each endpoint is included. A horizontal asymptote y=c becomes a vertical asymptote x=c, and conversely. To sketch: establish the original domain and key features, mark their reflected partners, draw the reflected curve on the swapped domain, then label the curves and y=x. For f(x)=2x+1, 0 <= x 1, the endpoints (0,1) and (1,3) become (1,0) and (3,1). Both remain included. Check: points fixed by reflection lie on y=x. For a strictly increasing function, intersections with its inverse lie on that line. For a decreasing function this conclusion need not hold: a self-inverse line can coincide with its inverse.