Formal Notation for Domain and RangeRelations vs. Functions (function notation)More Domain Practice

The set of all possible values of the independent variable in a function.

read “x such that x belongs to …”

“x such that x is greater than …”

{ | ____}x x

{ | ____}x x

{ | ____}x x

{ | ____}x x

{ | ____}x x

x such that x is greater than or equal to …

x such that x is less than …

x such that x does not equal … (implies x can be all other real numbers)

The set of all possible values of the dependent variable in a function.

read “y such that y belongs to …”

etc.

{ | ____}y y

A relation in which each value of x has a unique y value.

For example –

3 5y x y x

2 3 5x x y2 22 5x y

2 1y x2

2 3

4

xy

x

2 22 3 8x y2

33y x

(0)f

2( ) 2 1f x x x

2(0) 2(0) (0) 1f

(0) 1f

(1)f

2( ) 2 1f x x x

2(1) 2(1) (1) 1f

(1) 2 1 1f

(1) 2f

( 1)f

2( ) 2 1f x x x

2( 1) 2( 1) ( 1) 1f

( 1) 2 1 1f

( 1) 0f

( )f x

2( ) 2 1f x x x

2( ) 2( ) ( ) 1f x x x

2( ) 2 1f x x x

2( ) 2 1f x x x

( )f x

2( ) 2 1f x x x

2( ) (2 1)f x x x

2( ) 2 1f x x x

(2 1)f x

2( ) 2 1f x x x

2(2 1) 2(2 1) (2 1) 1f x x x

2(2 1) 2(4 1) 2 1 14f x x xx

2(2 1) 2(4 1) 2 1 14f x x xx

2(2 1) 8 2 28f x x xx

2(2 1) 8 210f x x x

( )f x h

2( ) 2 1f x x x

2( ) 2( ) ( ) 1f x h x h x h

2 2( ) 2( ) 12f x h x h x hxh

2 2( ) 2 2 14f x h x h x hxh

2

2( )

4

xf x

x( ) 2 5f x x

2 4 0x2 4x

2 4x

2x

Domain | 2x x

2 5 0x

2 5x5

2x

5Domain |

2x x

p. 68 # 1 – 4, 9 – 10, 14 – 15, 21, 27 – 39, 45, 47, 51, 55