lp presentations fnctions

General Mathematics

Grade 11

SAMPLE LESSON PLAN

1 2 3 4 5 -5 -4 -3 -2 -1

5

4

3

2

1

-1

-2

-3

-4

-5

Ordered Pairs

( x , y )Quadrant

I

Quadrant II

Quadrant III

Quadrant IV

( - , + )

( - , - ) ( + , - )

( + , +)

2nd coordinatey – coordinateordinate

1st coordinatex – coordinateabcsissa

X

y

Simple Recall:

T H S

I M M

A I A

N E P

A C T

T E B

C P M

O A Y

M L R

P R M

F S L

G B M

A O U

__ __ __ __ __ __

C P M

G E D

Z H M

A O R

O M A

P N S

S L M

E I R

O I O

S U E

B T C

L A N

E R N

S P Q

D R A

I A W

A = {(-3,-4), (-2,5), (-1,5), (0,6)}

B = {(-2,5), (0,5), (2,5), (4,5)}

C = {(0,3), (0,6), (-2,-4), (-4,-5)}

D = {(1,0) ( 0,1), (-1,0), (0,-1)}

Activity 2:

a.List down all first and second coordinates of each set

of ordered pairs and draw arrows showing the different

pairings.

b.Plot the given set of ordered pairs.

A = {(-3,-4), (-2,5), (-1,5), (0,6)}

B = {(-2,5), (0,5), (2,5), (4,5)}

C = {(0,3), (0,6), (-2,-4), (-4,-5)}

D = {(1,0) ( 0,1), (-1,0), (0,-1)}

Activity 2a:

-3

-2

-1

0

-4

5

6

A

-2

0

2

4

5

B

0

-2

-4

3

6

-4

-5

C

1

0

-1

0

1

-1

D

List down all first and second

coordinates of each set of ordered

pairs and draw arrows showing the

different pairings.

A = {(-3,-4), (-2,5), (-1,5), (0,6)}

B = {(-2,5), (0,5), (2,5), (4,5)}

C = {(0,3), (0,6), (-2,-4), (-4,-5)}

D = {(1,0) ( 0,1), (-1,0), (0,-1)}

Activity 2a:

-3

-2

-1

0

-4

5

6

A

-2

0

2

4

5

B

0

-2

-4

3

6

-4

-5

C

1

0

-1

0

1

-1

D

Functionor

NOT Function

Function Not FunctionFunction Not Function

A function is a set of ordered pairs (x,y) such that no two distinct members

have the same first element.

A = {(-3,-4), (-2,5), (-1,5), (0,6)}

B = {(-2,5), (0,5), (2,5), (4,5)}

C = {(0,3), (0,6), (-2,-4), (-4,-5)}

D = {(1,0) ( 0,1), (-1,0), (0,-1)}

Activity 2b:

CB D

A

Plot the given set of ordered pairs.

Activity 2b:

CB D

A

Functionor

NOT Function

Function NOT Function

Function

NOT Function

How can you determine whether the graph represents a function or not function?


(Vertical Line Test)A graph is a function if any vertical line

drawn passing through the graph intersects the graph at exactly one point.

Activity 2b:

CB D

A

Functionor

NOT Function

Function NOT Function

Function

NOT Function


Function

D

1234

R

-2-1012

X

1234

Y

-2-1012

Not Function

D 1 2 3 4 5

R -2 -1 0 -1 -2

X 0 1 2 2 3

Y 1 3 5 7 9

X -4 -2 0 -2 -4

Y 0 1 2 3 4

Function

Not Function

Not Function

Determine whether each of the following is a function or not. Click the letter of the correct answer.

2

4

6

8

3

5

7

9

1. a. FUNCTION

b. NOT FUNCTION

next


2

4

6

8

3

5

7

9

2. a. FUNCTION

b. NOT FUNCTION

next


2

4

6

8

3

5

7

9

3. a. FUNCTION

b. NOT FUNCTION

next


4.

a. FUNCTION b. NOT FUNCTION

next

{(1,3),(2,4),(3,5),(4,6),(5,7)}


4.


next

{(1,3),(2,4),(3,5),(4,6),(5,7)}

5. {(1,3),(1,4),(2,5),(3,6),(4,7)}


Identify which of the given graph represents a function.

a.

c.

b.

d.

Function Not Function


Which of the following ordered pairs are functions?

A = { (6, 6) , (4, 4) , (2, 2) , (0, 0) , (-2, -2) }

B = { (8, -4) , (6, -2) , (4, 0) , (2, 2) , (0, 4) }

E = { (1/2 , √3/2 ) , ( -1/2 , √3/2 ) ,

( -1/2 , - √3/2 ) , ( 1/2 , - √3/2 )

C = { (5, π) , (3, π) , (1, π), …}

D = { (1/2 , 1) , ( 1, 1/2 ) , ( -1/2 , 1) , ( -1, 1/2 ) }

Function

Not Function

Function

Function

Function

When is a set of ordered pairs represent a function?

“A set of ordered pairs (x,y)represents a function if and only ifno two distinct members have thesame first element.”

6.) ________________Not Function

A. Determine whether each of the following is a function or not.

X1

X2

X3

1

2

3

1.) ________________

X1

X2

X3

1

2

34

2.) ________________

X1

X2

X3

X4

1

2

3

3.) ________________

X1

X2

X3

X4

1

2

34

X1

X2

X3

1

2

34

5.) ________________

X1

X2

X3

X4

1

2

3

4.) ________________

FunctionFunctionFunction


B. Identify which of the given graph represents a function.

1.) ______________ 2.) ______________ 3.) ______________ 4.) ______________ 5.) ______________

10.) ______________9.) ______________8.) ______________7.) ______________6.) ______________

Function Not FunctionFunction

Function Function

Not Function Not Function

Not FunctionNot FunctionNot Function

1.) If a function is represented by a set of ordered pairs, then, no two pairs have the same second component. 2.) Every line on a Cartesian coordinate plane represents a function. 3.) The relation y = x is not a function.4.) An element of the range of a function may be used more than once.5.) The equation x2 + y2 = 1 represents a function.

Determine whether each statement is true or false. Explain each answer.

Thank you.

May Real

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