It is very tempting to think of a computer program as something that will "give you the answer." You can easily fall into the trap of acting as though using a computer makes it unnecessary to think. This is never a very sensible attitude--after all, a computer should help you to think, not save you from thinking--and in the case of this particular program, it would certainly not be justified.
For one thing, the method used by this program to draw graphs is precisely the one that you have probably learned is not effective: plotting a bunch of points on the graph and connecting them with lines. The results look OK most of the time because the program uses a fairly large number of points (one or two hundred or so), and because it tries to make some reasonable guesses about when not to draw connecting lines between a pair of points (when there is a jump in the function or a vertical asymptote, for example). However, this method of drawing graphs has an inescapable problem: if anything interesting happens between a pair of consecutive points, the program has no way of knowing it and it will not appear in the picture. A function that varies rapidly will not be drawn accurately. For example, if you graph sin(500*x) on the interval from -1 to 1, the result will be completely wrong and misleading, since the function goes up and down too rapidly to capture by plotting just a few hundred points. Some functions, such as sin(1/x), simply cannot be drawn accurately with a finite number of points.
Some problems can arise when you let the computer decide the maximum and minimum values for the y-axis of a graph. The computer will simply test a few hundred points and choose the largest and smallest values it finds. If the true maximum or minimum occurs between points, it will not be found. If you plot sin(x), for example, you might get a maximum value of 0.99928774 instead of 1. If you plot arcsin(x), the maximum value of π/2 will be missed by a much larger amount.
Besides these built-in limitations to the methods used, there are probably still some bugs--that is out-and-out programming errors--in the program that may cause it to give an incorrect answer (or even to crash your computer). You will be able to recognize blatant errors because you (presumably) understand what the computer is supposed to be doing and have some idea of what the answer might be. As for more subtle errors--well, just never trust a computer entirely.
