Functions and Their Properties

Def: Function, Domain and RangeA 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 thatassigns a unique element in R to each elementIn 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) = 24 x

Even and Odd Functions

• Even functions

• Odd functions

Piecewise-defined functions

• Graph 2

, 0

( ) ,0 1

1, 1

x x

y f x x x

x

Absolute value Function

• The absolute value function is defined piecewise by the formula

y x

, 0

, 0

x xx

x x

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