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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. .
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
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 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.