2.1.1 functions and their graphs
TRANSCRIPT
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Formal Notation for Domain and RangeRelations vs. Functions (function notation)More Domain Practice
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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
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{ | ____}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)
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The set of all possible values of the dependent variable in a function.
read “y such that y belongs to …”
etc.
{ | ____}y y
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A relation in which each value of x has a unique y value.
For example –
3 5y x y x
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2 3 5x x y2 22 5x y
2 1y x2
2 3
4
xy
x
2 22 3 8x y2
33y x
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(0)f
2( ) 2 1f x x x
2(0) 2(0) (0) 1f
(0) 1f
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(1)f
2( ) 2 1f x x x
2(1) 2(1) (1) 1f
(1) 2 1 1f
(1) 2f
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( 1)f
2( ) 2 1f x x x
2( 1) 2( 1) ( 1) 1f
( 1) 2 1 1f
( 1) 0f
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( )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
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( )f x
2( ) 2 1f x x x
2( ) (2 1)f x x x
2( ) 2 1f x x x
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(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
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( )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
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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
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p. 68 # 1 – 4, 9 – 10, 14 – 15, 21, 27 – 39, 45, 47, 51, 55