
Re: Simple analytical properties of n/d
Posted:
Mar 7, 2013 3:38 AM


On Wed, 6 Mar 2013, Ross A. Finlayson wrote: > > Exercise. Graph f:(R^2  Rx{0}) > R, (x,y) > x/y. > Mapping R^2 \ (0,0) the pointed disc to x/y, it is a manytoone > function where for each x =/= 0, for each r =/= 0 there is y s.t. for > each x/y = r. So its image is the four quadrants minus the axes.
What's a pointed disk? R^2\(0,0) is neither a disk nor pointed; it's a punctured plain. No. The image of f is R. R^2  both axis is not the image nor the graph. It's not even the projection of the graph onto the xyplain. . . which is R^2  the yaxis. The graph is a surface within xyz 3space. > What then of each r/y or x/r, as r ranges?
g(x) = x/a is linear; h(x) = b/x is hyperbolic.

