Slide 1 Peelschools org Function Function Notation by wuzhengqin

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									Function    Function Notation       Function Formula

y  x2     y  f [3( x  7)]  8   y  [3x  7 ]2  8
   1                                         2
y         y  4 f [2( x  1)]        y
   x                                       x 1

y     x      y  5 f ( x)  7        y 5 x 7

y  3x        y  f ( 2 x)  8         y  6x  8
1.4 – Domain & Range
Domain:                         Range:
- the x-values of a relation    - the y-values of a relation




          Determine the domain and range of
         the relations on the following pages.
                   Using set notation.
Two methods of expressing
        domain and range
                1. Set Notation
            2. Interval Notation
What is set notation?

Set Notation:
A set is merely a collection of elements or
 members. So in math it is a collection of
 numbers.
Set notation is like a special language that
 we use to express what domain and range
 is covered by a function.
What is interval notation

Interval notation is another way of defining
 domain and range… but it is more
 efficient!
  Open Parentheses ( )
     If the value is not included or undefined.
      (i.e. holes, asymptotes, or a jump)
  Closed Parentheses [ ]
     If the value is part of the graph.
 Interval Notation
   Infinities      or
      If the graph continues forever to the right or upwards,
       it approaches infinity.
      If the graph continues forever to the left or
       downwards, it approaches negative infinity.
   Union Sign
      If there is a break in the graph, join the interval up to
       and after that break with the union sign.


BUT, interval notation cannot be used for
discrete functions!
       Set Notation




‘x’ belongs to
the set of real
   numbers



      Domain = {xR}   Range = {yR}
Interval Notation




   Domain : x(,)
   Range : y(,)
Set Notation




                            ‘y’ is less than
                             or equal to 6




Domain = {xR}   Range = {yRy6}
Interval Notation




               Domain : [




   Domain : x(,)
   Range : y(,6]
   Set Notation

       {(2,4), (3,5), (4,6), (5,7)}

  Domain = {2,3,4,5}        Range = {4,5,6,7}
        OR                         OR

Domain : {x I 2  x  5}       Range: {y I 4  y  7}
Interval Notation

   {(2,4), (3,5), (4,6), (5,7)}


  Can’t use interval
  notation for integers!
Set Notation, because
integers

       3
       4                  -3
       5                   5


           D: {3, 4, 5}
           R: {-3,5}
    Set Notation




‘x’ is greater
 than -3, but
less than or
  equal to 5



                 D:{xεR | -3<x≤5}   R:{yεR | y=3}
Interval Notation

                    D:
                    R:
  Set Notation




Domain = {xR-4x4}   Range = {yR -4y4}
Interval Notation




                    Domain : x [ 4,4]
                    Range : y [ 4,4]
‘x’ belongs to
   the set of
    integers



Domain = {x-6x3}   Range = {y -1y8}
Set Notation


                     Asympotote
                   Where the graph
                approaches the line but
               never actually touches it.
Interval Notation?




                     D:
                     R:
What about equations?
     f ( x)  3 x  5
                            This is a linear function (not and not
a)                           vertical or horizontal), so x and y
                                      can be any value.

       Domain = {xR}          Range = {yR}



b)   g ( x)  2( x  1)  8
                        2
                                  • This is a quadratic function.
                                  • It opens upward, thus has a min.
                                  • The min. value is -8.


       Domain = {xR}          Range = {yRy-8}
  c)   h( x )      x9                         Are there any restrictions
                                               that must be placed on ‘x’,
                                                or will any ‘x’ value work
                      Can’t be -’ve                  in this function?




     So, what values of ‘x’ will not make the
    part under the squareroot sign negative?

Domain = {xRx-9}                   Range = {yRy0}
D:X ε [-9,+∞)                         R: Yε [0,+∞)

								
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