1. Find the value of y for each of the following values of x:#1 #2 #3
Find the value of x for each of the following values of y: #4 #5

2. Find the value of y for each of the following values of x:#1

3. Find the value of y for each of the following values of x:#1 #2

4. Find the value of y for each of the following values of x:#1 #2 #3

5. Find the value of x for each of the following values of y:#4 #5

6. Find the value of x for each of the following values of y:#4 #5

7. Find the value of y for each of the following values of x:#1 #2 #3
Find the value of x for each of the following values of y: #4 #5

8. Table x y

9. Table
Ordered Pair x y

10. Graph
Y-axis
Ordered Pair
X-axis

11. Vocabulary
relation
domain
range
function

12. A relationship is a situation that can be described by a set of linked data.
The data from a relationship can also be represented by a graph.
Relationships can also be represented by a set of ordered pairs called a relation.

13. Relationships can also be represented by a set of ordered pairs called a relation.
For example:
The scoring systems of a track meets is as follows:
1st place: 5 points
3rd place: 2 points
2nd place: 3 points
4th place: 1 point
This scoring system is a relation, so it can be shown as ordered pairs. {(1, 5), (2, 3), (3, 2) (4, 1)}.
You can also show relations in other ways, such as tables, graphs, or mapping diagrams.

14. {(1, 5), (2, 3), (3, 2) (4, 1)}.
Table
Graph
Mapping

15. {(1, 5), (2, 3), (3, 2) (4, 1)}.
Table
Graph
Mapping
Place
Points

16. {(1, 5), (2, 3), (3, 2) (4, 1)}.
Table
Graph
Mapping
Points
Place

17. {(1, 5), (2, 3), (3, 2) (4, 1)}.
Table
Graph
Mapping

18. Example 2: Showing Multiple Representations of Relations
Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram.
x y
Table
Write all x-values under “x” and all y-values under “y”. 2 4 6 3 7 8

19. Example 2: Showing Multiple Representations of Relations
Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram.
Graph
Use the x- and y-values to plot the ordered pairs.

20. Example 2: Showing Multiple Representations of Relations
Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram.
Mapping Diagram x y
Write all x-values under “x” and all y-values under “y”. Draw an arrow from each x-value to its corresponding y-value. 2 6 4 3 8 7

21. The domain of a relation is the set of first coordinates (or x-values) of the ordered pairs. The range of a relation is the set of second coordinates (or y-values) of the ordered pairs. The domain of the track meet scoring system is {1, 2, 3, 4}. The range is {1, 2, 3, 5}. Notice that domains and ranges can be written as sets.

22. Give the domain and range of the relation.1 2 6 5 –4 –1
Domain: {6, 5, 2, 1}
Range: {–4, –1, 0}

23. x y Give the domain and range of the relation. Domain: {1, 4, 8} 1

24. Give the domain and range of the relation.
The domain value is all x-values from 1 through 5, inclusive.
The range value is all y-values from 3 through 4, inclusive.
Domain: 1 ≤ x ≤ 5
Range: 3 ≤ y ≤ 4

25. A function is a special type of relation that pairs each domain value with exactly one range value.

26. Give the domain and range of the relation
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
{(3, –2), (5, –1), (4, 0), (3, 1)}
Even though 3 is in the domain twice, it is written only once when you are giving the domain.
D: {3, 5, 4}
R: {–2, –1, 0, 1}
The relation is not a function. Each domain value does not have exactly one range value. The domain value 3 is paired with the range values –2 and 1.

27. Give the domain and range of the relation
Give the domain and range of the relation. Tell whether the relation is a function. Explain. –4 2
Use the arrows to determine which domain values correspond to each range value. –8 1 4 5
D: {–4, –8, 4, 5}
R: {2, 1}
This relation is a function. Each domain value is paired with exactly one range value.

28. Give the domain and range of each relation
Give the domain and range of each relation. Tell whether the relation is a function and explain.
a. {(8, 2), (–4, 1),
(–6, 2),(1, 9)} b.
D: {–6, –4, 1, 8}
R: {1, 2, 9}
D: {2, 3, 4}
R: {–5, –4, –3}

29. Vocabulary relation domain range function All possible values of “x”
All possible values of “y”
A relation where each domain value maps into EXACTLY one value in the range.

30. Which relation is not a function:
Example 1
Which relation is not a function: A B
NOT C
Talk about height example if you don’t get slide made…

31. Give the domain and range of the graph.
Example 2
Give the domain and range of the graph.
YES
its a function!

32. Give the domain and range of the graph.
Example 3
Give the domain and range of the graph.
NOT
a Function!

33. y x Vertical Line Test If a vertical line touches
the graph of a relation in
more than one place the
graph is NOT a function x

34. Recognizing Functions

35. Lesson Quiz
Give the domain and range of the graph and identify if it is a function.
NOT
a Function!

36. Lesson Quiz
Give the domain and range of the graph and identify if it is a function.
NOT
a Function!

37. Lesson Quiz

38. Lesson Quiz

39. Lesson Quiz

40. Page 209: 15-25, and 32-38b