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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.

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