Summary: Domain and Range of Functions

Key Concepts

  • The domain of a function includes all real input values that would not cause us to attempt an undefined mathematical operation, such as dividing by zero or taking the square root of a negative number.
  • The domain of a function can be determined by listing the input values of a set of ordered pairs.
  • The domain of a function can also be determined by identifying the input values of a function written as an equation.
  • Interval values represented on a number line can be described using inequality notation, set-builder notation, and interval notation.
  • For many functions, the domain and range can be determined from a graph.
  • An understanding of toolkit functions can be used to find the domain and range of related functions.
  • A piecewise function is described by more than one formula.
  • A piecewise function can be graphed using each algebraic formula on its assigned subdomain.


interval notation
a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion
piecewise function
a function in which more than one formula is used to define the output
set-builder notation
a method of describing a set by a rule that all of its members obey; it takes the form [latex]\left\{x|\text{statement about }x\right\}[/latex]