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Parent Function Quiz

• 4 Graphs• No Calculators/No Notes• Use entire 10x10 grid• Don’t forget to graph asymptotes if needed!• About 8-10 minutes to complete

Homework Questions?

Relations and Functions

Chapter 2

Section 2-1

Pages 72-81

Objectives• I can determine if the relation is a

function by two methods.• I can find Domain and Range from

relations and continuous graphs• IMPORTANT VOCABULARY in

this section!!

Important Vocabulary

• Relation• Domain• Range• Discrete Function• Continuous Function• Vertical Line Test

1 2 63 4 5 7 8 9 10

4

3

2

7

56

8

9

x-axis

y-axis

0

1-2-6 -3-4-5-7-8-910

-4

-3

-2

-1

-7

-5

-6

-8

-9

0

-1

Quadrant I

(+, +)

Quadrant II

(-, +)

Quadrant IV

(+, -)

Quadrant III

(-, -)

Origin (0,0)

Relation

• A relation is a set of ordered pairs!

• Need the braces { } to show a set

• Example: { (1, 2), (3, 4), (5, 6) }

Domain and Range

• The domain in any relation is the first coordinates from the ordered pairs. It is the Input!

• Domain = X -Values• The range in any relation is the second

coordinates from the ordered pairs. It is the Output!

• Range = Y- Values

x-axis

DomainInput

Independent Variable

y-axisRange

OutputD

epen

dent

Var

iabl

e

Example 1: Domain/Range

• Given the following relation• {(2,3), (-4,8), (2,6), (7,-3)}• What is the Domain?• { -4, 2, 7}• **Notice they are listed least to greatest!! • No duplicates!!!• What is the Range?• {-3, 3, 6, 8}

Example 2:

• Given the following ordered pairs, find the domain and range.

• {(4,5), (-2,3), (5,6)}

• Domain is {-2, 4, 5}• Range is {3, 5, 6}

Answer Format• When listing a set of numbers for domain or range,

use the set symbols {}• List numbers from least to greatest (increasing

order). No duplicates!• Ex: the domain has numbers: 3, -2, 5, 2, 3

• {-2, 2, 3, 5}

4 Ways to see Relations

RelationsOrdered Pairs

{(2, 3),(-3, 1),(1, -2)} X Y

2 3

-3 1

1 -2

Data Tables

GraphsMapping

2

-3

1

3

1

-2

X Y

Function

• A function is a special relation in which• NO DUPLICATED “x-values”• Example: Is the following relation a function:

{ (1,3), (4,-9), (6,3) }• Answer: Yes. No x-values are duplicated

Ex 2: How about this relation. Is it a function?

• Given the following { (2,3), (-4,8), (2,6), (7,-3)}• Function: No.• The x-value “2” is duplicated

Tell whether the pairing is a function.

Identify a functionEXAMPLE 2

a.

NOT a function because the input “0” is paired with both 2 and 3.

b.

Identify a functionEXAMPLE 2

OutputInput

21

0 0

4 8

6 12

Function? Yes

GUIDED PRACTICE for Example 2

Tell whether the pairing is a function.

1221Output

12963Input2.

Function? Yes

GUIDED PRACTICE for Example 2

Tell whether the pairing is a function.

3210Output

7422Input3.

Function? No

Vertical Line Test

• You can use a vertical line test to easily see on a graph is the relation is a function.

• You place a straight edge like a pencil vertical on the graph and move it across the graph. If the line intersects the graph at only one point at a time, then it is a function.

Applying VLT

y 2 = x

x

y

Vertical Line Test

Consider the graphs.

x 2 + y

2 = 1

x

y

y = x 2

x

y

2 points of intersection

1 point of intersection

2 points of intersection

Discrete Function

•A function with ordered pairs that are just points and not connected.

Discrete Function

Continuous Functions??

• A function is continuous if it has an infinite domain and forms a smooth line or curve

• Simply put: It has NO BREAKS!!!

• You should be able to trace it with your pencil from left to right without picking up your pencil

27

x

y

4

-4

The domain of a continuous function is all x-values!We read domain from LEFT to RIGHT

The range of a continuous function is all the y-values!We read range from BOTTOM to TOP.

Domain

Range

x

y

– 1

1

Example: Find the domain and range of the function f (x) = from its graph.

The domain is [–3,∞).

The range is [0,∞).

3x

Range

Domain

(–3, 0)

These are "assumed" arrows!

The graph goes on forever.

Example 1Domain( , )

Range[ 3, )

Example 2

Domain( , )

Range( , 4]

Example 3

Domain[0, )

Range( , )

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Domain( , )

Range[2, )

6

4

2

-2

-4

-6

-5 5

Domain( ,3]

Range[1, )

Domain( , )

Range

[0, )

Domain( , 1) [1,6]U

Range( ,6)

What Graph Activity

• Graphs A – Q around the room.• Answer questions based on domain and

range.

Homework

• WS 1-4• Quiz Next Class