To use the Animate utility, choose the command "Animate" from the Utilities Menu. The menu bar will disappear, and the animate utility will fill the screen. This utility allows you to see a "moving picture" of a family of functions.
A mathematician might well say something like "consider the function f(x) = x^3-k*x, where k is a constant." Now, since k is clearly not a "constant" in the sense of being a known number, what can this mean? The mathematician really wants to consider ALL of the functions x^3-3*x, x^3-π*x, x^3+0.4*x, and so on for all the possible values of k. Presumably, the idea is to see what all these functions have in common, or perhaps to see how the value of k affects the result. We could say that the formula x^3+k*x really represents a "family" of related functions.
The Animate utility provides a way of viewing such a family of functions. It can draw the graphs of some of the functions in the family, and then flip through the graphs at high speed, providing an animation that can effectively illustrate how the value of k affects the appearance of the function.
The Animate utility has the usual boxes for specifying the maximum and minimum values for the x and y axes and a formula for the functions to be graphed. The formula, of course, should involve both x and k. You can also specify a starting and stopping value for k in the animation, and the number of frames that the animation should contain. If there are n frames, the range of k values is divided into (n-1) intervals and a graph is plotted for each of the n endpoints of these intervals. (For example, if n=5 and the range of k-values is from 0 to 1, then a graph is drawn for each of the values k=0, k=0.25, k=0.5, k=0.75, and k=1.)
To start the animation, just click on the Begin button. The computer will begin calculating the graphs--things will speed up once all the graphs have been calculated. You can stop the process at any time by clicking on the Stop button, and restart it with Begin. The Next button can be used to compute or display the graphs one at a time, rather than as an animation.
Note that you can type in new values and click on check boxes or buttons while an animation is in progress. If you change any of the values in the text-entry rectangles and then click on Begin or Next, a new animation will be started.
