MATH21 NOTES - Functions OBJECTIVES: Define a function and...

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Functions
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OBJECTIVES : Define a function and
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FUNCTIONS Ø Latin  functio  – first appeared in a mathematical  article  in  the  Acta  Eruditorem  to  denote  various  tasks  that  a  straight  line  may  accomplish  with  respect  to  a  curve,  such  as  forming  a  chord,  tangent, or normal.  Ø   The  Swiss  mathematician  Leonhard  Euler  in  1749 defined a function as a variable quantity that  is  dependent  upon  another  quantity,  thereby  approaching today’s definition.   The notation f(x)  is attributed to him and he wrote one of the most  influential algebra books of all time.
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FUNCTIONS Ø A  function  f  from  set  A  to  set  B  is  a  rule  of  correspondence  that  assigns  to  each  element  x  in  the  set  A  exactly  one  element  y  in  the  set  B. - set of ordered pairs ( x, y) such that no two pairs will  have  the  same  first  element. Set A 1 2 3 4 5 Set B 2 10 8 6 4
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Domain (set of all x’s) Range (set of all y’s) 1 2 3 4 5 2 10 8 6 4 Mapping of X- values into y-values ( 1 -1 correspendence) X Y
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Set A is the domain 1 2 3 4 5 Set B is the range 2 10 8 6 4 Mapping illustrating many – 1 correspondence
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1 2 3 4 5 2 10 8 6 4 Mapping of the elements of Set A in to Set B illustrating 1 – many type of correspondence. Set A Set B
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Characteristics of a Function Ø Each element in A (domain) must be matched with an  element of B (range). Ø Each element in A is matched to not more than one  element in B. Ø Some elements in B may not be matched with any element  in A. Ø Two or more elements of A may be matched with the same  element of B.
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  Function Notation We commonly name a function by letter.  Because  function starts with f, it is a commonly used letter to refer  to functions.  ( 29 6 3 2 2 + - = x x x f This means the right hand side is a function called f This means the right hand side has the variable x in it; x is the independent variable The left side DOES NOT MEAN f times x like brackets usually do, it simply tells us that what is on the right hand side is an expression in x. The left hand side of this equation is the function notation.  
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MATH21 NOTES - Functions OBJECTIVES: Define a function and...

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