Domain and Range of Functions

Definition of Domain and Range

• Function f(x): maps input x to output f(x)

• Domain: set of all possible inputs x that the function can take

• Range: set of all possible outputs f(x) for the inputs in the domain

Domain and Range of First Function

• Domain:

  • Defined for: [-4 \leq x < 8]

  • Note: Open circle at x = 8 (not included)

• Range:

  • Defined for: (2 < f(x) \leq 8)

  • Note: Open circle at f(x) = 2 (not included)

Domain and Range of Second Function

• Domain: All real numbers (function is defined for any x)

• Range: All real numbers (function increases and decreases indefinitely)