The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Simple analytical properties of n/d
Replies: 20   Last Post: Mar 11, 2013 11:01 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Simple analytical properties of n/d
Posted: Mar 7, 2013 3:38 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 many-to-one
> 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 xy-plain.
. . which is R^2 - the y-axis.
The graph is a surface within xyz 3-space.

> What then of each r/y or x/r, as r ranges?

g(x) = x/a is linear; h(x) = b/x is hyperbolic.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.