How to Calculate Domain & Range on a Graphing Calculator

Finding the domain and range of a function is one of the best ways to investigate the overall behavior of the function. In basic terms, the domain of a function is the range of possible x values that can be input into it, where x stands in for the independent variable. The range is the set of possible output values. So if the function is f(x) = x², the possible input values (the domain) are all real numbers, and the output values are all positive real numbers because a negative number squared gives a positive result. Finding the range of a function on a calculator isn't usually necessary, but you can use a graphing calculator to find it easily enough.

The first step to using your graphing calculator as a domain and range finder is to plot the equation in question into the calculator. This is accomplished differently depending on the model of calculator you're working with.

On a TI-84 or similar model, it is accomplished by pressing the "Y=" key and then entering the function you're looking to graph under "Y1," (although any other space is fine too because you can enter up to 10 equations at once) using "X, T, θ, n" to enter your variable, x. Press "Graph" to plot the function.

For a Casio model, like the FX-9750GII, enter the function under "Menu" and "Graph" and then enter the equation and press "F6" to plot it.

On an HP calculator, such as the HP-50g, hold the "Left Shift" key – an arrow going up and to the left – and press "F1." If an equation is displayed, press "Del" to remove it ("F3" on the calculator, below the on-screen option), and then press "Add"/ "F2" to enter your equation. Use "Draw"/ "F6" to plot it.

You don't need a domain calculator to find the domain of a function. In most cases, the domain is specified along with the equation – when it only applies for a limited range of x values, for example. In most cases, functions have a domain of all real numbers, but if x is in the denominator of a fraction, it can't apply to any values of x that would result in the denominator equaling zero.

Graphing calculators aren't perfectly set up for plotting the range of a function. The best thing you can do is plot the graph and inspect it or convert it into a table of numerical values to find the range of possible outputs. With your plotted graph, you can either visually inspect it to see the range of y values possible as an output or use your calculator's "Trace" function to get values for specific points on the graph. On a TI-84 or similar model, press the "Trace" button when the graph is on screen. On a Casio FX-9750GII, bring up this option by pressing "Shift" and "F1" together. On HP-50g calculators, press "F3." You then use the arrow navigation buttons to get numerical output values for each x value.

You can put these values into a table if you like, but the range is easy to determine; look for the smallest and largest values from the "Trace" function.