mac1140_lecture15_1

# mac1140_lecture15_1 - L15 3.2 Functions Definition A...

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123 L15 §3 .2 Func t ion s Definition . A function is a relation such that for each element in the domain there is only one element in the range. Function Notation: ( ) yf x = . If x is an element in the domain of f , then () x = is the corresponding element in the range. Thus, for a function, ab f a f b =⇒ = , that is, no two ordered pairs have the same first coordinate . Which of the following are functions? ( ) ( ) { } 1,1 , 2, 2 , 3, 3 ,. .. f = ( ) ( ) { } 5,5 , 2, 3 , 5, 5 ,. g =− ( ) ( ) { } 1,1 , 4,6 , 6,4 , 1, 2 ,. .. h { (, ) } kx yy x ==

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124 Example . Determine which of the following relations are functions? a) 2 yx = b ) = c) 2 x y = d ) 2 = + Analytical Test: If a relation is given by an equation , and if the equation can be solved for y and there is only one real solution, then the relation is a function .
125 Vertical Line Test: If each vertical line intersects the graph of a relation at no more than one point, the relation is a function . Example : 22 (3 )(1 )4 xy −+ += Example: Determine which of the sketches below represent functions.

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126 Think of ( ) fx as a rule. Don’t forget the order of operations!
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mac1140_lecture15_1 - L15 3.2 Functions Definition A...

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