Domain and range

Math

Definition

The domain of a function is the set of all possible input values (x-values), and the range is the set of all possible output values (y-values). Restrictions on domain typically come from division by zero, square roots of negatives, or logarithms of non-positive numbers.

Examples

  • f(x) = √x has domain [0, ∞) and range [0, ∞)
  • f(x) = 1/x has domain (-∞, 0) ∪ (0, ∞), excluding x = 0
  • f(x) = x² has domain (-∞, ∞) and range [0, ∞)

Related Terms

Function notation Inverse functions Piecewise functions Composition of functions

Study This Concept

Practice domain and range with free review games in these units:

Pre-Calculus Unit 1: Functions and Their Graphs