Functions and Their Properties

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# Functions and Their Properties - PowerPoint PPT Presentation

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

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### 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.

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.

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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
• What is Domain?
• What is Range?
• Find the Domain and Range of f(x) =
Even and Odd Functions
• Even functions
• Odd functions
Absolute value Function
• The absolute value function is defined piecewise by the formula
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.