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Understanding Functions and Their Properties

Learn about functions, domains, ranges, and different ways to test for functions. Identify bounded, unbounded, open, and closed intervals. Find domain and range of functions, even and odd functions, piecewise-defined functions, composite functions, and absolute value functions.

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Understanding 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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