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```					Introduction to Function

Irma Crespo & Larisa Yezersky
The Pascal Triangle
Input =1st diagonal column number                          3
Output = number in the diagonal column                     INPUT         OUTPUT

2
1                      1
1

Output
1        1                                 2                      1
1        2        1
1
1       3        3        1                        3                      1
1       4        6        4       1
1       5       10       10       5       1
0   4                      1
1 6 15 20 15 6 1
1   2     3        4       5
1 7 21 35 35 21 7 1
5       Input          1
Crespo 2009
The Pascal Triangle
Input = diagonal column number
80
Output = sum of the numbers in the                                  INPUT          OUTPUT
70
diagonal column                                                   1                     8
60
50
2                    28
1

Output
1        1                             40        3                    56
1        2        1                        30        4                    70
1       3        3        1
1       4        6        4       1
20
5                    56
10
1       5       10       10       5       1                      6                    28
1 6 15 20 15 6 1                                          0

1 7 21 35 35 21 7 1                                             0    72     4            6 8     8    10

8          Input      1
Crespo 2009
Function Rules to Live By
A function is a rule that
establishes a relationship                                  Input   Output
between two quantities,
called the input and the                                     0         3
output.                                                      1         1
2         2
For each input, there is                                     3         3
exactly one output.                                          4         4
5         8
There can be more than
one input for the same
output.                                                             Crespo 2009
- Larson et.al. Algebra 1. 2001. McDougall Littell
Function Rules to Live By
Domain
The domain is the collection of all input values of the
independent variable that determines the value of other
variables.
INPUT        1          2            3
OUTPUT           7          8            9
12
Domain
10

8                                            Input
Output

6
Independent
4
Variable
2

0                                         x-axis values
0           1     2     3       4
Crespo 2009
Input
Function Rules to Live By
Range
The range is the collection of all output values of the
dependent variable whose value is determined by the
independent variable.
INPUT       1            2            3
OUTPUT          7            8            9
12                                            Range
10

8
Output
Output

6
Dependent
4
Variable
2

0                                         y-axis values
0           1     2      3        4
Crespo 2009
Input
Function Junction

THE WORD PROBLEM
A cell phone company charges \$80 for a
phone. Its minutes for talk time are charged at
a rate of \$0.50 per minute up to 300 minutes.
The total cost c of the phone and the number
of minutes m is given by the function:
c = \$80 + \$0.50m
If you maximized the talk time minutes, how
much could have your parents paid?
Crespo 2009
Make the Connection
List
Make a list of inputs (m), use the function to calculate an
output (c) and use the rule: 60 ≤ m ≤ 300 to fill in 5 values
at most for each input, function, and output columns.
INPUT INPUT \$80 OUTPUT
c=       + \$0.50m            OUTPUT
m = 60   c = \$80 + \$0.50 (60)          c = 110
m = 120       c = \$80 + \$0.50 (120)   c   = 140
m = 180       c = \$80 + \$0.50 (180)   c   = 170
m = 240       c = \$80 + \$0.50 (240)   c   = 200
m = 300       c = \$80 + \$0.50 (300)   c   = 230
Crespo 2009
Make the Connection
Table
Record the values into an input/output table.

m      60      120     180     240     300

c      110     140     170     200     230

Crespo 2009
Make the Connection
Graph
Cost per Minute of Cell Phone Use
250

200
costs (c) in
dollars

150

100

50

0
60
1     120
2        180
3      240
4   300
5

time in
minutes (m)
Crespo 2009
Make the Connection
Domain and Range
The domain of the function is all values of m such
that 60 ≤ m ≤ 300 which are:

m       60     120      180     240     300

c      110     140      170     200     230

The range of the function is all values of c as
shown above.
Crespo 2009
Make the Connection

What do the domain and
range mean in the
problem?

Crespo 2009
Quick Run

Off to the whiteboard
for a brief revisit.

Crespo 2009
Practice the Function

The student government in Pratts High School is facing
a dilemma on fundraising. It has to unlock the answers
to the Tangram Puzzle in order to fulfill all the school
improvement projects for the school year that require
\$5,000 in the student government treasury. Currently, it
only has \$1,500 in the coffer. It profits \$500 per
fundraiser. Represent the number of fundraising events
with E and the money gained for the treasury with T.

Crespo 2009
Complete the Tangram

1.3 Illustrate
the algebraic
1.2 Indicate                                                  model.
the labels            1. Scramble for the function
by creating an equation
1.1. Show the verbal model.

2. Create an
input/output table for
3. Represent the
the equation.
table with a labeled
line graph.                                                4. How many
fundraising events
will it take to reach
its target?

Crespo 2009
Tangram Solutions
Money gained for the treasury is equal to the money in the
treasury at the beginning plus the profits from a fundraiser times the
number of fundraising events.
number of fundraising events = E
money in the treasury at the beginning = \$1,500
profits from a fundraiser = \$500
money gained for the treasury = T

T = \$1,500 + 500E where \$1,500 < T ≤ \$5,000

E         1         2         3         4         5         6            7
T       \$2000     \$2500     \$3000     \$3500     \$4000     \$4500        \$5000

Crespo 2009
Tangram Solutions
Money in the Treasury Per Fundraising Event
6000
Money in the Treasury (T) in \$

5000

4000

3000

2000

1000

0
1        2       3         4        5       6         7

Number of Fundraising Events (E)

The student government needs 7 fundraising events to reach its
target.
Crespo 2009
What’s Behind the Tangram?

Crespo 2009
What’s Behind the Tangram?

Crespo 2009
The Matching
Time for Fun!!!

Crespo 2009
Exit Slip

Crespo 2009
Acknowledgement

Larson, R.,Boswell L., Kanold, T., & Stiff, L. (2001).
Algebra 1. Illinois: McDougall Littell.
Microsoft Office for cliparts and base template.
PowerPoint created by I.S.Z.B.Crespo.
List, tables, graphs, equations, word problems,
tangram puzzle, and worksheets are original
creations.
Lesson plan strictly made by Irma Crespo.

Crespo 2009
Thank you!

A Lesson Plan Presentation

By

Irma Crespo & Larisa Yezersky

Crespo, Yezersky

```
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