Mathematical expressions and functions are graphed using a computer implemented method that automatically determines an appropriate graph range. One implementation of the method begins with determining an initial variable seed range. A number of points within this seed range are randomly selected. The method determines whether the selected points correspond to the mathematical expression (i.e., whether they produce valid results when the expression is evaluated at each point). When the selected points produce valid results, the points can be used to generate and display a graph of the mathematical expression on a user display device, with a graph range based on the seed range. If not, the variable seed range can be expanded until a predetermined number of the selected points correspond to the mathematical expression, so that a graph of the mathematical expression can be generated and displayed.