In order to see a graph on the calculator, you must have the appropriate window. When you press the key you see seven settings. 99% of the time, you will only use the first six.
A standard window setting is usually
- Xmin and Xmax set the boundaries for the x–axis
- Ymin and Ymax set the boundaries for the y–axis
- Xscl and Yscl settings determine the increment by which the axes are marked
This means the x and y axes both go from –10 to 10 and are marked off in increments of 1. A non-calculator notation for this is: x:[-10, 10] x 1 (read as xscl = 1 or by 1) and y:[-10, 10] x 1 (read as yscl = 1 or by 1).
The viewing window on the calculator is 95 pixels in the x–direction and 63 pixels in the y–direction. One pixel in each direction is used by the axes, so you have 94 x-pixels and 62 y-pixels available. This doesn’t effect your graph or how it looks, but it can be useful information when using the button.
Graph y = x + 3 in a standard window. For information on graphing functions, click here.
Press and then use the and keys to see x and y values at the bottom of your screen.
Notice these x and y values have many decimal places and are not necessarily values we are interested in.
Press and reset the values to x:[-9.4, 9.4] y:[-9.3, 9.3] and then re-graph the line. Now pressing and the and keys will show you values at the bottom of the screen that are easier to work with. These values are usually much more useful to you when solving problems too.
Because of the nice looking numbers you see while tracing, many people call the window you just used a “friendly” window.
For simple functions, a standard window or a friendly window should be sufficient. For more complicated functions, window adjustments will probably have to be made.
For example, graphing the function y = 3x3 - 5x2 + 22x - 64 in a friendly window gives you
Obviously this window is not appropriate. But how should it be changed? One way to figure out new window settings is to press and see what x and y values the function is producing.
Clearly our y settings are way off base. If we adjust the y settings to y:[-1000, 1000] x 100 we get a graph that looks like this.
If you reset your window and still have trouble seeing a complete graph, keep changing numbers until you get an appropriate graph. Don’t get too frustrated. This is one of the most difficult things to do when the function requires a dramatic change in the window setting.
Another way to figure out new window settings is by looking at a table of values using the TABLE feature. To find out more, click here to go to the table lesson.
As you can see, the window settings play a key role in graphing. You can adjust the settings to have nice x and y values when tracing. In some cases, adjusting the window is necessary just to see the graph. When you press and see something unexpected (or nothing at all) your first response should always be to check the window settings.