M. Pickens ©2006

Domain and RangeDomain and Range

Part 1Part 1

M. Pickens ©2006

ObjectivesObjectives

• To learn what domain and range areTo learn what domain and range are• To determine the domain and range of a To determine the domain and range of a

table, equation, word problem, set of table, equation, word problem, set of coordinates.coordinates.

M. Pickens ©2006

Function Machine

Input

Output

IN

Out

x

Y or f(x)

Independent Variable

Dependent Variable

Domain

Range

M. Pickens ©2006

What are Domain and Range?What are Domain and Range?

• DomainDomain• The possible values for the independent The possible values for the independent

variable (the possible x values)variable (the possible x values)

• RangeRange• The possible values for the dependent variable The possible values for the dependent variable

(the possible y values)(the possible y values)

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Domain and Range of a TableDomain and Range of a Table• In a table the independent variable is on the ________ In a table the independent variable is on the ________

and the dependent variable is on the ________.and the dependent variable is on the ________.• So the values for the domain are on the _________ So the values for the domain are on the _________

and the values for the range are on the __________.and the values for the range are on the __________.

leftright

leftright

PinksPinks WinksWinks

-2-2 44

-1-1 66

00 88

11 1010

22 1212

Domain : _______________

Range: _________________

{-2, -1, 0, 1, 2}

{4, 6, 8, 10, 12}

# of Roses# of Roses DollarsDollars

11 55

22 1010

33 1515

44 2020

55 2525

Domain : _______________

Range: _________________

{1, 2, 3, 4, 5}

{5, 10, 15, 20, 25}

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Domain and Range of an EquationDomain and Range of an Equation

• In an equation the __________ variable is by itself. It In an equation the __________ variable is by itself. It is what the equation figures out. The ____________ is what the equation figures out. The ____________ variable is what is plugged variable is what is plugged ininto the equation.to the equation.

• Recall: Domain = ___________ Range = _________Recall: Domain = ___________ Range = _________

dependentindependent

independent dependent

2rA Dependent Independent

Domain:All possible values for r

Range:All possible values for A

pz 6Dependent Independent

Domain:All possible values for p

Range:All possible values for z

M. Pickens ©2006

Domain and Range of a Word ProblemDomain and Range of a Word Problem

James sold CD’s for $5 each after he paid $15 James sold CD’s for $5 each after he paid $15 for equipment and supplies. Write an equation for equipment and supplies. Write an equation showing his profit. Then give the Domain and showing his profit. Then give the Domain and Range.Range.

P = 5c – 15c = # of CDs soldP = profit

InputOutput

The Domain is all possible c or input valuesDomain: possible # of CDs soldDomain: whole numbers {0,1,2,3,4….}

The Range is all possible P or output valuesRange: possible profit valuesRange: {-15, -10, -5, 0, 5, 10, 15, 20…}

M. Pickens ©2006

Domain and Range of a Set of CoordinatesDomain and Range of a Set of Coordinates

• What are the domain and range of the What are the domain and range of the following set of coordinates?following set of coordinates?

• (4, -7), (-3, 9), (2, 0), (7, 4), (-1, 9)(4, -7), (-3, 9), (2, 0), (7, 4), (-1, 9)

Domain- all the possible x values Range- all the possible y values

Domain: {4, -3, 2, 7, -1}

Range: {-7, 9, 0, 4}

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Mixed PracticeMixed Practice

• What are the domain and range of the What are the domain and range of the followingfollowing

52 th 16Dependent Independent

Domain:All possible values for t

Range:All possible values for h

TimeTime HeightHeight

00 -5-5

11 1111

22 5959

33 139139

44 40914091

Domain : _______________

Range: _________________

{0, 1, 2, 3, 4}

{-5, 11, 59, 139, 4091}

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Mixed PracticeMixed PracticeLina’s cell phone company charges her 10 cents Lina’s cell phone company charges her 10 cents

per minute plus a $5 service charge each per minute plus a $5 service charge each month. She can figure out her bill by the month. She can figure out her bill by the equationequation

C = 0.10m + 5C = costm = # of minutes used

Give the Domain and Range of the situation(assume the company rounds to the nearest minute)

Domain= input= possible # of minutesDomain= whole numbers {0, 1, 2, 3 …}

Range= Output= possible cost of bill

Range = {$5, $5.10, $5.20, $5.30, $5.40 …}

M. Pickens ©2006

Mixed PracticeMixed Practice

• Give the domain and range of the followingGive the domain and range of the following

{(-3, -7), (4, 16), (-0.1, 0), (4, 9), (-2, 3)}{(-3, -7), (4, 16), (-0.1, 0), (4, 9), (-2, 3)}

Domain: {-3, 4, -0.1, -2}

Range: {-7, 16, 0, 9, 3}

{(-½ , 15), (40, 700), (9.2, 90), (8, -10)}{(-½ , 15), (40, 700), (9.2, 90), (8, -10)}

Domain: {-½, 40, 9.2, 8}

Range: {15, 700, 90, -10}

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Mixed PracticeMixed Practice

• What is the domain and range?What is the domain and range?

x

yList the coordinates

(-7, 3), (-4, 6), (-3, -5),

(-2, 2), (2, 4), (4, -2),

(5, 6)

Domain: {-7, -4, -3, -2, 2, 4 ,5}

Range: {3, 6, -5, 2, 4, -2}

M. Pickens ©2006

Mixed PracticeMixed Practice

• If the domain of y = 3x + 4 is {-1, 3, 5} If the domain of y = 3x + 4 is {-1, 3, 5} what is the range?what is the range?

• If the range of y = 3x + 4 is {-1, 3, 5} what If the range of y = 3x + 4 is {-1, 3, 5} what is the domain?is the domain?

x values

y valuesy = 3(-1) + 4 = 1y = 3(3) + 4 = 13y = 3(5) + 4 = 19

Range: {1, 13, 19}

y values

x values

-1 = 3x + 4-4 -4-5 = 3x 3 3 x = -5/3

3 = 3x + 4-4 -4-1 = 3x 3 3 x = -1/3

5 = 3x + 4-4 -4 1 = 3x 3 3 x = 1/3

Domain: {-5/3, -1/3, 1/3}

M. Pickens ©2006

ConclusionConclusion

• Domain is -Domain is -

• Range is -Range is -

The possible values for the independent variable

(the possible x values)

The possible values for the dependent variable

(the possible y values)