# How to Calculate Domain & Range on a Graphing Calculator

The domain and range indicate some boundaries and constraints of a function. The domain of a function is the set of x values for which the function returns a result. The range of a function is the set of all y values returned over the domain. Different types of functions have different trends that determine their domain and range. On a graphing calculator, you can determine the domain and range visually or by looking at the graph's table.

### Things You'll Need

- Graphing calculator

#### Step 1

Enter the function in your graphing calculator's function menu. On a Casio fx-9750GII or related model, press "Menu" and select "Graph." On a TI-84 plus or related model, press "Y=." On an HP-50g, hold the left shift button and then press "F1". Then, press "F2" to enter a function.

#### Step 2

View the graph of the function. On a Casio fx-9750GII, press "F6" after entering your function. On a TI-84 plus, press "Graph." On an HP-50g, press "F6" after entering the function. Sometimes, you can get a sense of the domain and range just by looking at the graph. For example, the function y=x^2 is a parabola with a vertex at the origin. Its domain is all real numbers, and its range is from zero to infinity.

#### Step 3

Trace the function. On a Casio fx-9750GII, press "Shift" and "F1." Then select "Trace." On a TI-84 plus, press "Trace." On an HP-50g, press "F3." This feature will give you a sense of the general behavior of the function. For example, the y values of y=log(x) tend towards negative infinity as x goes to zero. Because x never equals zero, the domain of the function is all positive real numbers. As you trace the function and monitor y values, you will notice that the range includes all real numbers.

#### Step 4

Look at the table of values for your graph. On a Casio fx-9750GII, press "Exe" while tracing the line. This command will store values. Press "Optn" and then "F1" to view the table. On a TI-84 plus, press "2nd" and then "Trace." On an HP-50g, press the left shift button and then "F6." The table will help confirm the trends that you viewed while tracing the graph.

### Tips & Warnings

- If the y-value of a function is undefined for a particular x-value, that x-value is not in the domain of a function.
- As you gain more experience looking at the general behavior of different types of graphs, you will notice patterns. Take note of those patterns, as they will help you quickly estimate the approximate domains and ranges of similar functions.