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.

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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.

Slide 1- 2 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 Vertical line test Ordered pairs (if an x value is repeated) Finding specific domains

Bounded, Unbounded, Open, Closed intervals

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

Piecewise-defined functions Graph

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 composition f 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.

Hwk. p. 19, #1-53 e.o.o.,51,57-62