The set of all input values that are allowed are called the domain of the function. The domain is defined by

• restrictions due to the function rule;

• restrictions due to the situation.

The domain of a function $f$ is written as ${\text{D}}_f$.

The set of all possible function values is called the range of the function. In order to determine the range of a function $f$ you need a complete graph of $f$. It is important that the vertices of the graph are visible. At a vertex, the function has a (local) maximum (largest function value) or a (local) minimum (smallest function value). The range of a function $f$ is written as ${\text{B}}_f$.

You often use interval notation to show the domain and range of a function.
An interval is a continuous set of real numbers, a stretch of the number line. The set of real numbers is written as $ℝ$.