1. Coordinate System Review
By Mrs. Swanberg
2002

2. (left or right, up or down)
(x, y)
(left or right, up or down)
(run, jump)
(domain, range)

3. Plot the following ordered pairs.
B(4, -6)
C(-6, 2)
D(6, 2)
E(-4, -6)
F(0, 6)
Connect the points in alphabetical order.

4. Quadrants I II x
III IV y

5. Next 2 clean pages in your notebook!

6. Relations and Functions

7. Relation Any set of ordered pairs.
For each first member there may be MANY second members.

8. Domain
The possible set of all the input values for the independent variable in a given situation
The set of first coordinates.

9. Range
The possible set of all the output values for the dependent variable in a given situation.
The set of second coordinates.

10. 2
Domain 7
+ 5
Range

11. Annual Household Waste
Country
Annual Domestic Waste
Equivalent per Person (lbs)
France
15,500
634
Great Britain
15,816
620
Japan
40,225
United States
200,000
1925
West Germany
20,780
741
{(15500, 634), (15816,620), (40225, 634),
(200000, 1925), (20780, 741)}

12. Annual Household Waste
Domain
First coordinate
x-value
15,500
15,816
40,225
200,000
20,780
Range
Second coordinate
y-value
634
620
1925
741

13. x y 1 -1 3 4 7 {(1, -1), (1, 3), (4, 7), (-1, 7)} Domain {1, 4, -1}
Express the relation shown in each table as a set of ordered pairs. Then state the domain and range of the relation. x y 1 -1 3 4 7
{(1, -1), (1, 3),
(4, 7), (-1, 7)}
Domain {1, 4, -1}
Range {-1, 3, 7}

14. x y 2 3 6 -1 {(2, 3), (6, -1), (2, -1)} Domain {2, 6} Range {3, -1}
Express the relation shown in each table as a set of ordered pairs. Then state the domain and range of the relation. x y 2 3 6 -1
{(2, 3), (6, -1),
(2, -1)}
Domain {2, 6}
Range {3, -1}

15. Function
A relation in which for each first member there is one and only one second member.

16. Vertical Line Test
Can be used to determine if a relation is a function.
For every function, the vertical line passes through only ONE point on the graph.

17. Use the vertical line test to determine if the relations on the next 2 slides are functions.

18. AND A RELATION
Function

19. A RELATION
NOT A FUNCTION

20. Graph each relation. Then determine if each relation is a function.x -1 4 5 y -4 -5
Yes; it is a function because
each element of the domain
is paired with exactly one
element in the range.

21. A Function {(-1, -1), (0, 0), (4, -4), (5, -5)} -1 -1 -4 4 -5 5 Range
Domain -1 -4 -5 -1 4 5

22. Graph each relation. Then determine if each relation is a function.x 1 2 y 4 -2 -4
No; it is not a function because
the element 1 in the domain
maps to both 4 and -2
in the range.

23. 1 2 Not a Function {(1, 4), (0, 0), (1, -2), (2, -4)} 4 -2 -4 Range
Domain 4 -2 -4 1 2

24. Is this a function?
{(1, -2), (0, 0), (2, -2)}
Range
Domain 1 2 -2

25. Some relations are functions.

26. All functions are relations.