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Functions and Their Properties

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

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Functions and Their Properties

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  1. 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.

  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. .

  3. Ways to test for a function • Vertical line test • Ordered pairs (if an x value is repeated) • Finding specific domains

  4. Bounded, Unbounded, Open, Closed intervals

  5. Identifying Domain and Range of a Function • What is Domain? • What is Range? • Find the Domain and Range of f(x) =

  6. Even and Odd Functions • Even functions • Odd functions

  7. Piecewise-defined functions • Graph

  8. Absolute value Function • The absolute value function is defined piecewise by the formula

  9. 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.

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

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