# Probability

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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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