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Functions and Their Properties. Def: Function, Domain and Range

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functions and their properties

Functions and Their Properties

Def: Function, Domain and Range

A function from a set D to a set R is a rule that assigns to every element in D a unique element in R. The set D of all input values is the domain of the function, and the set R of all output values is the range of the function.


A function from a set D to a set R is a rule that

assigns a unique element in R to each element

In this definition, D is the domain of the function and R is a set containing the range in D.


ways to test for a function
Ways to test for a function
  • Vertical line test
  • Ordered pairs (if an x value is repeated)
  • Finding specific domains
identifying domain and range of a function
Identifying Domain and Range of a Function
  • What is Domain?
  • What is Range?
  • Find the Domain and Range of f(x) =
even and odd functions
Even and Odd Functions
  • Even functions
  • Odd functions
absolute value function
Absolute value Function
  • The absolute value function is defined piecewise by the formula
composite functions
Composite Functions
  • Let f and g be two functions such that the domain of f intersects the range of g. The compositionf of g, denoted f ° g, is defined by the rule
  • (f ° g) = f ( g (x))).
  • The domain of f ° g consists of all x-values in the domain of g that map to g(x)-values in the domain of f.