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25 Piecewise- defined Functions

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					2.5 Piecewise- defined Functions
Quiz
 Have you taken your Exam 1 yet?
Piecewise-Defined Function
                                          y
 example                                 5
                                          4

                                          1

                                                               x
                                    -2        1         5


    f(x) = x2




                f(x) = x2 if -2 ≤ x ≤ 1                x2 if -2 ≤ x ≤ 1
                                              f(x) =
                f(x) = x if 1 < x ≤ 5                  x if 1 < x ≤ 5
    f(x) = x
Piecewise-defined Function
 Definition: a Piecewise-defined Function is a function
  defined by different rules over different subsets of its
  domain

 Typical example: f(x) = |x|
  we can rewrite f(x) = |x| into piecewise-defined form as:


                            x if x ≥ 0
                   f(x) =
                            -x if x < 0
Graph a piecewise-defined Function

 Example:
              x+3     for -3 ≤ x < -1
   f(x) =     5       for -1 ≤ x ≤ 1        Notice: When
              √x      for 1 < x < 9      meeting with ‘<’ or
                                        ‘>’, use ‘ 。’ to mark
                                            the end point .
                                        Other cases, use ‘ . ’.
 1, What is the domain?
 2, What is the range?
 3, Find f(0)
 4, Find f(-5)
 5, Find f(-1)
Graph of the Piecewise-defined Function
 Sketch the graph of the piecewise defined function:



                     4      for x ≤ 0
            f(x) =   - x2    for 0 < x ≤ 2
                     2x - 6 for x > 2
Find The Formula For a Piecewise-defined
Function
                               y
 Example:


          -x2 +3    if x ≤ 0
 f(x) =
          (1/3)x-1 if x > 0


                                           x
Homework
 PG. 132: 6-24(M3), 33, 36, 37, 52

 KEY: 15, 36, 52

 Reading: 2.6 Combinations

				
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Jun Wang Jun Wang Dr
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