Mathematics 4 You

There is a lot of great software for graphing available on the Internet. Here is some of the best that I have found.

Graph

This program by Ivan Johanson is a basic graphing utility that does its job quite effectively. It is just 2D but has many quality features such as animations, arc lengths, areas, tangents, and normals. It supports functional, parametric, polar, and relational graphing.
It is free and open source: licensed under the GNU General Public License.
It is quite fast but the program is quite small.
It is easy for the beginner to learn, but does not offer the features that a power user may be looking for.
The GUI is very easy to learn.
It is windows based.
It is not very customizable, but it is very portable having almost no registry keys except perhaps a file association to .grf

3D-XplorMath-J© is a Java based program.
It is free and easily downloaded.
It is fairly fast and has easy rotation function.
It is more like a gallery of 3D Images. It has many pre-set functions but not many new functions can be created.
It is very end user oriented, with a click and view layout.
The GUI is basically menu based.
Because it is java based it runs on both Mac and Windows.
It is not easily customized but it is portable, downloadable as a single executable.

Graphing calculator 3D by Runiter© company comes in two versions the free version and the paid version.
The free version is somewhat limited in its functionality. Although it has excellent color and graphics it does not support discontinuity checking or parametric graphing in the free version.
It is quite fast graphing the equation while it is being typed at any point where it creates a valid mathematical function.
It does not contain the features a power user would need in the free version.
The GUI is very user oriented with colorful button style options.
It is also windows based.
It is not portably self contained - requiring Java to be installed.

It comes bundled with Microsoft Office.
Its graphs are very slow but powerful allowing great customization of the data.
It can be used by the beginner and power user alike but the power user will get much more out of it.
The graph GUI is not as smooth as some of the other options listed here and is more challenging to work with.
It runs on either Windows or Macintosh.
It is not at all portable but is greatly customizable.

It is not extremely fast but has good colors in its graphing utility. It is user oriented but command line underneath. It is quickly confused when trying to graph relations, so power users may find it insufficient for their projects. The GUI is somewhat nonstandard, providing a large virtual calculator, which shows nothing on the screen, as well as a confusing layout of overlapping tabs.
It is also a Microsoft product which limits its use on Linux and other open source OSes.
It is not very customizable or portable.

Sage is a powerful math and graphing tool designed for Linux.
It is free and open source - licensed under the GNU GPL
It is fairly fast and powerful - even when virtualized.
It is necessary to learn the command line to use it so the beginner may have a bit of a learning curve, but it provides many powerful features for the power user and programmer.
The GUI is basically a web page with text boxes that accept command line arguments for the functions to be graphed.
As a web page or as a virtual machine it can be run on almost any platform or OS.
The options are also command line with dynamic scalability.
As a virtual machine it is fairly portable from a power user’s perspective.