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# Functions and Their Properties - PowerPoint PPT Presentation

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

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Presentation Transcript

### 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.

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• Vertical line test

• Ordered pairs (if an x value is repeated)

• Finding specific domains

• What is Domain?

• What is Range?

• Find the Domain and Range of f(x) =

• Even functions

• Odd functions

• The absolute value function is defined piecewise by the formula

• 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.