A few years ago, a friend sent me a copy of some software he had designed, and which his son had programmed. This article is not a detailed review of GrafEq, but rather a cursory description of what graphing programs do, and a hint at what sets GrafEq apart from others of its kind.

First, a few necessary introductory paragraphs to put things in context

Graphs, in the context of high school algebra, are pictorial representaions of numbers, sets of numbers, ranges and relations.

So: x = -3, x = 7.5, x = {1,7,11}, x < 2, x <= 4, x > 7, 5 < x < 7 and so on, can all be pictorially represented on a horizontal numberline. Further discussion of this topic is too elementary to be of use here.

In the context of high school mathematics, graphs are usually thought of as illustrations of the numerical relationship between variables, and are drawn on the coordinate plane. The numerical relationships are expressed as relations, sometimes referred to as equations such as y = 2x - 8 and so on.

These relationships can be classified as being either functions or not functions. A function of x, for example is explained as a relation between x and y which is such that for every x there is one and only one corresponding y value. So, y = x^3/10 is a function of x.

Such functions are easily plotted by any graphing software or graphing calculators. Often, one wishes to have two such functions displayed together. Most graphing software could not handle the following illustration beacause in the "blue" relation, each x has none or two values of y. Not a problem for GrafEq:

Also notice that the functions are written in "standard mathematical notation", as opposed to

y = x^3/10

GrafEq includes what has got to be the worlds easiest-to-use equation editor. The resulting graphs are vector graphics and components such as arrows etc. are easily added.

As is standard with such software, the ranges of the axes, the presence and frequency of "ticks" and the colour of the graphs is customizable.

Two graphs often have points in common, and finding the coordinates of these points is a common objective of high school math courses. This can be done by what might be called "algebraic manipulation" or it may be done graphically. The hesitation over using the graphical approach is that this does not lead to an "accurate" result. My comments on this criticism are discussed elsewhere.

Here we see an illustration of the first of several qualities that sets GrafEq aprt from the rest of the herd. One can zoom in on the intersection point and determine the coordinates of the corners of the pixel of intersection at whatever magnification is desired. There are a host of implications of that statement - but the simple, bottom-of-the-line translation is that the coordinates of the point of intersection are easily determined to whatever degree of precision is required.

Most graphing programs have a host of limitations. For example, many are not capable of dealing with closed curves such as ellipses; and often the relationship between the variables must be expressed in a y = f(x) form. Not so GrafEq:

 How about plotting regions with multiple constraints? Have a look at this one. The constraints indicated in the second quadrant is the actual input to the software entered via the equation editor.

If you want to take a closer look, start here: http://www.peda.com/grafeq/gallery.html