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					                                        Wed, 9/28
    SWBAT… graph piecewise functions
Agenda
1.   Warm Up (10 min)
2.   Quiz (20 min)
3.   Graphing (15 min)




Warm-Up:
1.) Turn in HW#7 in the blue folder
2.) Review your graphing linear equations
    using a table of values and absolute value
    notes including transformations


          Review PPT3: Piecewise functions
1.) Cut a piece of graph paper into 4 squares
2.) On one graph paper square:
   1. Graph x = 3
   2. Graph y = -2
3.) On another graph paper square,
   graph y = x + 1



       Review PPT 3: Piecewise functions
                                          Wed, 9/28
    SWBAT… graph piecewise functions
Agenda
1.   Warm Up (10 min)
2.   Piecewise functions (35 min)




Warm-Up:
1.) Cut a piece of graph paper into 6 squares
2.) On one graph paper square:
    1. Graph x = 3
    2. Graph y = -2
3.) On another graph paper square,
    graph y = x + 1

              HW#5: Piecewise functions
 Graphing Horizontal & Vertical Lines
                                                  y
When you are asked to graph a
line, and there is only ONE
variable in the equation, the line
will either be vertical or horizontal.
For example …
                                                            x
          Graph x = 3
    Since there are no y–values in       y = –2
  this equation, x is always 3 and y
   can be any other real number.


          Graph y = –2
  Since there are no x–values in
 this equation, y is always –2 and
                                                      x=3
 x can be any other real number.
                                          Thurs, 9/29
    SWBAT… graph piecewise functions
Agenda
1.   Warm Up (10 min)
2.   Piecewise functions (35 min)




Warm-Up:
1.) On one graph paper square:
    1. Graph x = -5
    2. Graph y = 1
2.) On another graph paper square,
    graph y = x + 1
3.) On a number line graph x > 3

              HW#5: Piecewise functions
                                               y

       Graph x = -5
Since there are no y–values in this
equation, x is always -5 and y can
    be any other real number.                      y= 1
                                                          x

         Graph y = 1
Since there are no x–values in this
 equation, y is always 1 and x can
    be any other real number.




                                      x = -5
Step 1: Solve for y

Step 2: Look at the y-intercept (b) and
                                                                     y=x+1
plot where the graph crosses the y-axis.              y
                                                      5

                                                      4
Step 3: Use the slope
(rise/run) to determine
                                                      3

the next point and plot.                              2

     Slope = 1 = 1/1                                   1

                             -5   -4   -3   -2   -1    0 1   2   3   4   5
                                                                             x
Step 4: Draw a line                                   -1

through both points. Be                               -2
sure to extend the line                               -3
and put arrows at both
ends. (Use a ruler!)
                                                      -4

                                                      -5


Step 5: Label your line
    Endpoints when graphing
<       >          ≤          ≥
          Endpoints when graphing
    <         >          ≤                  ≥
Open Circle Open Circle Closed circle Closed circle
    Piecewise Function
    A piecewise function is any function that is in, well, pieces!
    Piecewise functions indicate intervals for each part of the
     function



                      1     x3
Graph f(x) =          
                       x 1 x  3
Step 1:               Step 2 :            Step 3:              Step 4:

                      Erase part of the   Graph f(x) = x + 1 Erase part of the
Graph f(x) = 1        graph where x >3                       graph where x<3




                                 y

       1     x3
f(x) = 
       x  1 x  3                                 f(x) = 1

                                                      x
Step 1:          Step 2 :            Step 3:              Step 4:
                                     Graph f(x) = x + 1
Graph f(x) = 1                                            Erase part of the
                 Erase part of                            graph where x<3
                 the graph
                 where x >3




                                 y

       1     x3
f(x) = 
       x  1 x  3                                 f(x) = {1 x < 3

                                                      x
                                       3
Step 1:         Step 2 :           Step 3:            Step 4:

Graph f(x) = 1 Erase part of the                      Erase part of the
               graph where x >3    Graph f(x) = x + 1 graph where x<3




                            y
                                             f(x) = x + 1
       1     x3
f(x) = 
       x  1 x  3

                                               x
Step 1:         Step 2 :            Step 3:           Step 4:
Graph f(x) = 1 Erase part of the Graph f(x) = x + 1
               graph where x >3                       Erase part of the
                                                      graph where x<3




                                y

       1     x3
f(x) = 
       x  1 x  3                               f(x) = {x+1   x>3

                                                       x
                                              3
 Summary of steps for our example
            1     x3
     f(x) = 
             x 1 x  3
Step 1:          Step 2 :            Step 3:              Step 4:

Graph f(x) = 1   Erase part of the   Graph f(x) = x + 1   Erase part of the
                 graph where x >3                         graph where x<3
More Examples
   Go to the following website for more examples on
    graphing piecewise functions:
   http://archives.math.utk.edu/visual.calculus/0/functions.1
    3/index.html
The graph shows the monthly fee for Cell Zone. Use it to
answer the following questions:
 1) What is the monthly fee?
 2) How many minutes are included in the monthly fee?
 3) If a customer goes over the minutes included in the fee,
how much will they be charged per minute ($/min)?
 4) Write a function for this plan.
               80

               60
         Fee
         ($)   40

               20



                    100   200 300 400 500 600 700 800

                            Peak Minutes (minutes)

				
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