This activity allows the user to see functions typed in as algebraic expressions graphed on the coordinate plane.

The software graphs functions in basically the same way we would do it on paper. Axes are drawn, and a scale is set - based on the input in the range boxes. Next a table of x values between the two specified limits is generated, and then corresponding y values are calculated. Points are plotted, dots are connected, and the graph is displayed.

So what is different? Here is the big difference in the way the software works: We would probably plot 5 to 10 points and use our "math intuition" to connect the points appropriately. The computer plots many more points (depending on the x range, somewhere around 100) and connects the dots. This is how graphing calculators work, too.

This can lead to interesting behavior for certain functions. Polynomials like lines and parabolas will graph just as they should. Other functions, such as those for which x appears in a denominator, may have places on the graph where the computer has trouble plotting them correctly. This leads to the following moral: