C. Domain and Range

  • The domain and range identify the set of values for which the variables in a function are defined. The domain identifies all possible input values. These input values are often denoted by x (or some other appropriate independent variable, such as n from Example 3 in section B and are represented on the horizontal axis of the Cartesian coordinate plane. The input values correspond to the first coordinate in the ordered pair (x, y).

  • The range identifies all possible output values. These output values are often denoted by y (or some other appropriate dependent variable, such as T(n) from Example 3 in section B) and are represented on the vertical axis of the Cartesian coordinate plane. The output values correspond to the second coordinate in the ordered pair (x, y).

Example 1

State the domain and range for the following function.

The graph of the function extends indefinitely to the left and down as well as and to the right and up as indicated by the arrows on each end. As such, there are no restrictions on either of the variables.

When there are no restrictions on the variables in a function, the input and output can take on any Real Number values, R.

The above notation is read as "x such that x is a member of the set of real numbers" and "y such that y is a member of the set of real numbers".