How to Calculate Domain & Range on a Graphing Calculator

Graphing calculators can help you observe and check the domain and range.

The domain of a function is the set of all X values that are true for a specific function. The range is a set of all Y values that are true for a specific function. These two function characteristics are easy to calculate, however, special features available on most graphing calculators can help you observe and check the domain and range without any guesswork.

Instructions

1. Press the "Y=," or "Function" button, on the graphing calculator. Use the variable button ("X," "T," "?" or "n") and other necessary buttons to enter the function.

2. View the graph of the function.

3. Change the window parameters so that the graph fits in the window by changing the "Window" settings of the calculator. The standard window settings are Xmin = -10, Xmax = 10, Ymin = -10, Ymax = 10.

4. Evaluate the domain and range, and make an educated guess by looking at the graph. If you are graphing X^2, you can observe that the domain includes all integers for X, because the graph is clearly continuous on both the positive and negative sides of the X-axis. Conversely, you can see that the range includes all Y values greater than or equal to zero, as the graph does not extend downward, below Y = 0, at any point.

5. Use the "Table" feature of your graphing calculator to check the domain and range you have evaluated by entering the table settings. Be sure the Independent (Y) and Dependent (X) variables are set to "Automatic" (meaning the calculator enters the values for you), and change the settings to increments of 0.1, for X.

6. View the table. Scroll through the table to be sure that there is a Y value for every X value indicated.

Tips & Warnings

• If you cannot get a good idea of what your graph looks like from the graphing calculator, plug different numbers into the "Window" settings. For example, if it appears that the graph is far too big for the window, make the X and Y values larger. Use your judgment, and play around with the numbers until you get a good picture of the graph of the function.

• Make sure the function is entered correctly. If you use parentheses, pay extra attention to how the function is entered.

Resources

• Read this Article in Spanish
• Cool Math: Graphing Calculator