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Stand SW 100
Relation and function
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2. The cartesian products is written as A x B
Exercises A1
The cartesian products is written as A x B
1. A = {3,4 ,5} and B = { x , y }
1.A x B = { (3 ,x),(3,y),(4,x),(4,y),(5,x),(5,y)}
A = {6,8} and B {1,4,7}
2.A x B = { (6 ,1),(6,4),(6,7),(8,1),(8,4),(8,7)}
3. A = {1,5,7,9} and B = { 2 , 5 }
3.A x B = { (1 ,2),(1,5),(5,2),(5,5),(7,2),(7,5) ,(9,2),(9,5)}
4. A = {m,n} and B {2,4,8}
4.A x B = { (m ,2),(m,4),(m,8),(n,2),(n,4),(n,8)}
5. A = {3,6,9} and B = { 1 , 2 , 5 }
5.A x B = { (3 ,1),(3,2),(3,5),(6,1),(6,2),(6,5),(9,1) ,(9,2),(9,5)}

3. Relations & Functions Relation: a set of ordered pairs
Domain: the set of x-coordinates
Range: the set of y-coordinates
When writing the domain and range, do not repeat values.

4. Relations and Functions
Given the relation:
{(1, 2), (2, 3), (2, 4), (3,4), (1, 3), (3, 1)}
State the domain:
D: {1, 2, 3}
State the range:
R: {1,2, 3, 4}

5. Relations and Functions
Given the relation:
{(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)}
State the domain:
D: {0,1, 2, 3}
State the range:
R: {-6, 0, 4}

6. Do the ordered pairs represent a function?
Example 1
Do the ordered pairs represent a function?
writing the domain and range, do not repeat values.
r = {(-2, 5), (5,7), (0,1), (4, -2)}
Solution -2 5 4 5 7 1 -2
Yes, no x-coordinate is repeated.

7. Do the ordered pairs represent a function?
Example 2
Do the ordered pairs represent a function?
writing the domain and range, do not repeat values.
r = {(-5, 3), (0,3), (6, 3)} -5 6
Solution 3
Yes, no x-coordinate is repeated.

8. Do the ordered pairs represent a function?
Example 3
Do the ordered pairs represent a function?
writing the domain and range, do not repeat values.
r = {(0, 1), (0,2), (1, 3), (2,4)}
Solution 1 2 3 4 1 2
No, 0 is repeated in the domain.

9. Do the ordered pairs represent a function?
Example 4
Do the ordered pairs represent a function?
writing the domain and range, do not repeat values.
Mathematics
English
Thai
Science
Edwin
Richard
john
No, Edwin is repeated in the domain.

10. Mapping
{(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 1 3 -6 4

11. Functions
A function is a relation in which the members of the domain (x-values) DO NOT repeat.
So, for every x-value there is only one y-value that corresponds to it.
y-values can be repeated.

12. Functions Discrete functions consist of points that are not connected.
Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.

13. Do the ordered pairs represent a function?
{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)}
No, 3 is repeated in the domain.
{(4, 1), (5, 2), (8, 2), (9, 8)}
Yes, no x-coordinate is repeated.

14. Exercises 4.1 Page 124 3.We find that the following diagram
Homework
Page 124
3.We find that the following diagram
Relationship is a function ? 1 2 a b c 1 2 3 a b c 1 2 3

15. Exercises 4.1 Page 124 3.We find that the following diagram
Relationship is a function ? 3 a b C d 1 2 3 4 4 a b C d 1 2 3 4

16. a b d c 1 2 4 3 a b c d e 1 2 4 3 A B A B Exercises 4.1 Page 125
4.Relationship given in tabular form.
Relationship is a function ? 2 A B a b d c 1 2 4 3 1 A B a b c d e 1 2 4 3

17. a d c 1 2 3 a b c d e 1 3 2 4 5 A B A B Exercises 4.1 Page 125
4.Relationship given in tabular form.
Relationship is a function ? 4 A B a d c 1 2 3 3 A B a b c d e 1 3 2 4 5

18. 5.Do the ordered pairs represent a function?
Exercises 4.1
Page 125
5.Do the ordered pairs represent a function?
writing the domain and range, do not repeat values.
1. {(2,10), (3,15), (4, 20)}
2. {(-7,3), (-2,1), (-2, 4), (0,7)}
3. {(-2,1), (2,1), (4, 1), (-3,1)}
4. {(5,0), (3,-1), (0, 0), (5,-1), (3, -2)}

19. Caerfully your assignments
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Stand SW 100
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