Introduction to Function

Irma Crespo & Larisa Yezersky

The Pascal Triangle

Input =1st diagonal column numberOutput = number in the diagonal column INPUT OUTPUT

1 1

2 1

3 1

4 1

5 1

0

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3

1 2 3 4 5

Input

Outpu

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The Pascal TriangleInput = diagonal column number

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INPUT OUTPUT

1 82 283 564 705 566 287 88 1

Output = sum of the numbers in the diagonal column

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InputOutpu

t

Function Rules to Live By

A function is a rule that establishes a relationship between two quantities, called the input and the output.

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Input

3

1

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8

Output

For each input, there is exactly one output.

There can be more than one input for the same output.

- Larson et.al. Algebra 1. 2001. McDougall Littell

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Function Rules to Live ByDomain

The domain is the collection of all input values of the independent variable that determines the value of other variables.

INPUT 1 2 3INPUT 1 2 3OUTPUT 7 8 9

Domain

Input

Independent Variable

x-axis values0

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0 1 2 3 4

Input

Output

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Function Rules to Live ByRange

The range is the collection of all output values of the dependent variable whose value is determined by the independent variable.

OUTPUT

Range

Output

Dependent Variable

y-axis values

INPUT 1 2 3OUTPUTINPUT 1 2 3

OUTPUT 7 8 9

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0 1 2 3 4

Input

Output

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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?

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Make the ConnectionList

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 OUTPUTINPUT c = $80 + $0.50m OUTPUTINPUT c = $80 + $0.50m OUTPUT

m = 60

m = 120

m = 180

m = 240

m = 300

c = $80 + $0.50 (60) c = 110

c = $80 + $0.50 (120)

c = $80 + $0.50 (180)

c = $80 + $0.50 (240)

c = $80 + $0.50 (300)

c = 140

c = 170

c = 200

c = 230

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Make the ConnectionTable

Record the values into an input/output table.

m

c

m 60 120 180 240 300

c 110 140 170 200 230

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1 2 3 4 560 120 180 240 300

Make the ConnectionGraph

Cost per Minute of Cell Phone Use

time in minutes (m)

cost

s (c

) in

dolla

rs

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Make the ConnectionDomain 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.

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Make the ConnectionYour Interpretation

What do the domain and range mean in the

problem?

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Quick Run

Off to the whiteboard for a brief revisit.

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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.

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Complete the Tangram

1. Scramble for the function by creating an equation 1.1. Show the verbal model.

1.2 Indicate the labels

1.3 Illustrate the algebraic

model.

2. Create an input/output table for

the equation.3. Represent the

table with a labeled line graph. 4. How many

fundraising events will it take to reach

its target?

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Tangram SolutionsMoney 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 7T $2000 $2500 $3000 $3500 $4000 $4500 $5000

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Tangram Solutions

Number of Fundraising Events (E)

Mon

ey in

the

Trea

sury

(T) i

n $

Money in the Treasury Per Fundraising Event

The student government needs 7 fundraising events to reach its target.

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What’s Behind the Tangram?

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What’s Behind the Tangram?

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The MatchingTime for Fun!!!

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Exit Slip

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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.

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Thank you!

A Lesson Plan Presentation

By

Irma Crespo & Larisa Yezersky

Crespo, Yezersky