UNIT 2 : BASIC FUNCTIONS

8/16/2019 UNIT 2 : BASIC FUNCTIONS

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BASIC FUNCTIONS


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TERM & DEFINITION

TERM

DOMAIN

CODOMAIN

OBJECTIMAGE

RANGE


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• a

• b

• c• d

•

•

• •

A

B

CD

P Q

domain codomain

range

image

object


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• Domain : x = {1, 2,3,5}

• Codomain : y = {4,8, 9,25}

• Image : 4, 9, 25

• Object : 1, 2, 3, 5

• Range : Ry = {4,9,25}

• 4

• 8

• 9• 25

•

•

• •

1

2

53

x y

Square of


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RELATIONS

One-to-one

One-to-many

Many-to-one

Many-to-many


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One-to-one

• b

• a

• c• d

•

•

• •

A

B

DC

x y

small letter


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one-to-many

• -9

• -5

•-3

• -1

• 1

•

3• 5

• 9

•

•

• •

81

25

91

x y

x2


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many-to-one

x y

type of unit

• length

•

mass• currency

•

•

• •

•

•

•

Kg

m

inchkm

RM

g$


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many-to-many

character category

Type of character

• Superhero

• Princess

• Girl

• Guy

•

• •

•

ultraman

CinderellaSpiderman

Snow white


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TYPES OF FUNCTIONS


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LEARNING OUTCOME

IDENTIFY

DOMAIN &RANGE

SKETCHGRAPH

IDENTIFY

TYPE OFFUNCTION


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TYPE OFFUNCTION

LINEAR QUADRATICS MODULUS

LINEAR QUADRATICS


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LINEAR FUNCTIONS


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Example 1

Find the domain and the range for the function

→ 2 − 6, ∈ , 0 ≤ ≤ 4. .Sketch the graph.

(0 , −6)

(4 , 2)

TWO POINTS

SOLUTIONS

0 = 2 0 − 6 = −6

4 = 2 4 − 6 = 2

Y-intercepts = -6

x-coordinate y-coordinate


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2 64-4-6 -2

-2

-6

-4

2

6

4

y

x

(0 , -6)

(4 , 2)

Domain = Df = 0 ≤ ≤ 4, ∈

Range = Rf = −6 ≤ ≤ 2, ∈


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Exercise 1a (Tuto 2.3 / pg 38)


→ 4 − 3, ∈ , −1 ≤ ≤ 2. .Sketch the graph.

SOLUTIONS x-coordinate y-coordinate

−1 = 4 −1 − 3 = −7 (−1 , −7)

2 = 4 2 − 3 = 5 (2 , 5)

TWO POINTS

Y-intercepts = -3


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1 53-3-5 -1

-3

-5

1

5

3

y

x

(−1 , -7)

(2 , 5)

Domain = Df = −1 ≤ ≤ 2, ∈

Range = Rf = −1 ≤ ≤ 5, ∈

-7


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Example 1


→ 2 − 6, ∈ , 0 ≤ ≤ 4. .Sketch the graph.

(0 , −6)

(4 , 2)

TWO POINTS

SOLUTIONS

0 = 2 0 − 6 = −6

4 = 2 4 − 6 = 2

Y-intercepts = -6



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Example 3


→ |2 − 6|, ∈ , 0 ≤ ≤ 4. .Sketch the graph.

(0 , 6)

(4 , 2)

TWO POINTS

SOLUTIONS

0 = |2 0 − 6| = | − 6 |=6

4 = 2 4 − 6 = |2 |=2


Y-intercepts = 6

x-intercepts = 0 = 2 − 6

2 = 6

= 3


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MODULUS LINEAR


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2 64-4-6 -2

-2

-6

-4

2

6

4

y

x

(0 , -6)

(4 , 2)

Domain = Df = 0 ≤ ≤ 4, ∈

Range = Rf = 0 ≤ ≤ 6, ∈

3


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2 64-4-6 -2

-2

-6

-4

2

6

4

y

x

(0 , -6)

(4 , 2)

Domain = Df = 0 ≤ ≤ 4, ∈

Range = Rf = −6 ≤ ≤ 2, ∈


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QUADRATIC


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MODULUS QUADRATIC

UNIT 2 : BASIC FUNCTIONS

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