Functions by ferda.gurcan

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									 3-4 Functions
  3-4 Functions




                  Warm Up
                  Problem of the Day
                  Lesson Presentation




 Course
Course 33
 3-4 Functions

   Warm Up

   What three terms come next?

   1. 9, 12, 15, 18, . . .   21, 24, 27

   2. –8, –3, 2, 7, …        12, 17, 22

   3. 9, 10, 12, 15, 19, … 24, 30, 37




Course 3
 3-4 Functions


       Problem of the Day
       Sandra, Greg, and Michael team up for
       a competitive eating contest. If Sandra
       can eat 3 hot dogs per minute, Greg
       can eat 4 hot dogs per minute, and
       Michael can eat 5 1 hot dogs per minute,
                          2
       how long will it take them to
       eat a combined total of 100 hot dogs?
       8 minutes


Course 3
 3-4 Functions




  Learn to represent functions with tables,
  graphs, or equations.




Course 3
 3-4 Functions

                  Vocabulary
       function
       input
       output
       domain
       range
       vertical line test


Course 3
 3-4 Functions


       A function is a rule that relates two
       quantities so that each input value
       corresponds to exactly one output
       value.
       The domain is the set of all possible
       input values, and the range is the set
       of all possible output values.




Course 3
 3-4 Functions


      Functions can be represented in many
      ways, including tables, graphs, and
      equations. If the domain of a function
      has infinitely many values, it is
      impossible to represent them all in a
      table, but a table can be used to show
      some of the values and to help in
      creating a graph.




Course 3
 3-4 Functions
               Additional Example 1: Finding Different
                   Representations of a Function
  Make a table and a graph of y = 3 – x2.
  Make a table of inputs and outputs. Use the table to
  make a graph.

           x        3 – x2     y
           –2     3 – (–2)2   –1
           –1     3 – (–1)2   2
           0       3 – (0)2    3
           1       3 – (1)2    2
           2       3 – (2)2   –1

Course 3
 3-4 Functions
                   Check It Out: Example 1

  Make a table and a graph of y = x + 1.
  Make a table of inputs and outputs. Use the table to
  make a graph.
                                              y

           x    x+1      y
                                          3
       –1      –1 + 1    0
           0    0+1      1                            x
                                     –3           2
           1    1+1      2
           2    2+1      3



Course 3
 3-4 Functions


       If a relationship is a function, each
       input has exactly one output. When the
       relationship is graphed, use the
       vertical line test. Place a vertical line
       on the graph. If the line intersects the
       graph at only one point, then the
       relationship is a function. If the line
       intersects the graph at more than one
       point, then the relationship is not a
       function.

Course 3
 3-4 Functions




                 11
Course 3
 3-4 Functions
      Additional Example 2A: Identifying Functions

   Determine if the relationship represents a
   function.


           x   y   The input x = 2 has two outputs, y
           2   3   = 3 and y = 6. The input x = 3
                   also has more than one output.
           3   4
           3   5   The relationship is not a function.
           2   6



Course 3
 3-4 Functions
      Additional Example 2B: Identifying Functions

  Determine if the relationship represents a
  function.

                            The input x = 0 has two
                            outputs, y = 2 and y = –2.
                            Other x-values also have
                            more than one y-value.

                            The relationship is not a
                            function.



Course 3
 3-4 Functions
     Additional Example 2C: Identifying Functions
   Determine if the relationship represents a
   function.
   y = x3
   Make an input-output table and use it to graph y = x3.
      x          y
       –2      (–2)3 = –8
       –1      (–1)3 = –1
           0    (0)3 = 0
           1    (1)3 = 1
     2       (2)3 = 8
Each input x has only one output y.
The relationship is a function.
Course 3
 3-4 Functions
               Check It Out: Example 2A

   Determine if the relationship represents a
   function.


           x   y
                      Each input x has only one output
           0   0      y.
           1   1
                      The relationship is a function.
           2   2
           3   3


Course 3
 3-4 Functions
                 Check It Out: Example 2B

   Determine if the relationship represents a
   function.
                     y


                                 Since the relationship is
                2                linear there can only be one
                             x   output y for each input x.
           -2            2

                -2               The relationship is a function.




Course 3
 3-4 Functions
              Check It Out: Example 2C

   Determine if the relationship represents a
   function.
   y=x–1
                 x     x–1        y
                 0     0–1       –1
                 1     1–1        0
                 2     2–1        1
                 3     3–1        2
 Each input x has only one output y. The
 relationship is a function.
Course 3
 3-4 Functions
                   Lesson Quiz: Part I

   1. Graph the function y = x2 – 3.
                                  y

                             4


                             2

                                              x
                   -4   -2            2   4

                             -2

                             -4




Course 3
 3-4 Functions
                    Lesson Quiz: Part II

    Determine if each relationship represents a
    function.
    2.

           no

    3. y = 3x + 5

         yes




Course 3

								
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