Functions

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					  Functions

    ►Defining a function
  ►Using function notation
►Matching functions to graphs
             What is a function?
►Arule or a process which gives EXACTLY
 ONE output for EVERY input.

     Input        Function                       Output




                  In order for this to be defined as a
                  function, there must only be one
                  unique possibility for this output.
           What is a function?
► Isy = 3x + 2 a function?
► Lets try x = 6 as our input

       6           3x + 2         20




►No   matter what value we would have
used for our input, the output would
have been unique. Therefore it can be a
rule for a function.
            What is a function?
► Isy = +-x a function?
► Lets try x = 4 as our input

       4            x             2 or -2



►Positive input values always give two
solutions and negative values would give
no solutions so y = +-x is not a rule for
a function.
               Activity 1
 Time allowed – 5 minutes


►Turn to page 6 of your Core 3
 book and answer questions A1,
 A2 and A3
         Defining a function
► Thedefinition of a function consists of two
 parts:

 The Rule   How function is calculated
 The Domain Set of values which rule is
            applied to
               The Domain
► When  defining a function you MUST specify
  the set of input values to be used (domain).

► Ifthe domain is omitted we assume the
  function is defined for all values.
               The Domain
► Y=x    generates one value of y for all inputs
  greater than or equal to 0.
► If x is negative we get no solution. So this,
  on it’s own, would not give a function.
► However, if we state that the domain is the
  set of values where x ≥ 0, we can now
  define this as a function.
                 The Rule
► We   usually use letters to stand for
  functions, commonly f, g or h.
► If we call the square root function f, we can
  write it as.
► f (x) = x , x ≥ 0




  Rule                Domain
        Putting into context..
► The  context of a question can sometimes
  restrict the domain.
► g (x) = x3 can be defined for all values.
► If the above was applied to finding the
  volume of a cube of side x, then it wouldn’t
  be appropriate to include negative values in
  our domain.
               Activity 2
 Time allowed – 3 minutes


►Turn to page 8 of your Core 3
 book and answer question A4.
                Graphing a function
Sketch the graph of y = f (x) where f (x) = x2 - 2 , x ≥ -2




  Shown for all real values               Shown for f (x), where
  of x.                                   x ≥ -2. Why is there a
                                          closed circle at (-2,2)?
      Notation
means ‘x belongs to the set of
real numbers’




Can also be written
               Activity 3
 Time allowed – Rest of lesson


►Turn  to page 9 of your Core 3
 book and answer questions in
 Exercise A. Finish for
 homework.

				
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posted:6/4/2012
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