The document discusses relations and functions. A relation is a set of ordered pairs where the first elements comprise the domain and the second elements comprise the range. A function is a special type of relation where each domain element is paired with exactly one range element. The vertical line test can be used to determine if a relation is a function by seeing if a vertical line can intersect more than one point. Several examples of relations and functions are provided and it is asked whether the relations are functions using the vertical line test.

1. Relations and Functions
Objective: To use tables and graphs
to represent relations and functions.

2. 5-Minute Check
Solve each equation or inequality.
2. 3x – 2 = 13

3. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5

4. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21

5. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3

6. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3

7. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3 x = -2

8. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3 x = -2
• -12x > -24

9. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3 x = -2
• -12x > -24 x<2

10. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3 x = -2
• -12x > -24 x<2
• 7x < 2x – 25

11. 5-Minute Check
Solve each equation or inequality.
• 3x – 2 = 13 x=5
• 6 – 5x = 21 x = -3
• (2x + 7)/3 = x + 3 x = -2
• -12x > -24 x<2
• 7x < 2x – 25 x < -5

12. Relations and Functions
A Relation is a set of ordered pairs. The set of the
first coordinates is called the domain of the
relation. The set of the second coordinates is
called the range of the relation.

13. Relations and Functions
x y
Example:
-4 5
-2 6
0 2

14. Relations and Functions
x y
Example:
-4 5
-2 6
Domain: {-4, -2, 0}
0 2

15. Relations and Functions
x y
Example:
-4 5
-2 6
Domain: {-4, -2, 0}
0 2
Range: {5, 6, 2}

16. Relations and Functions
A Function is a relation in which each element of
the domain is paired with exactly one element in
the range.

17. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

18. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

19. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

20. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

21. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

22. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

23. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5

24. Relations and Functions
x y
-4 5
Example: -2 6
0 2
1 7
3 -5
The vertical line test can be used to determine if the
relation is a function. Use a straight edge moved slowly
across the graph to see if two point touch the edge at
the same time. This is a true test for all functions.

25. Relations and Functions
5. x y
3 -4
Example: -1 7
-6 -8
1 11
4 13

26. Relations and Functions
x y
3 -4
Example: -1 7
-6 -8
1 11
4 13
Domain: {-6,-1,1,3,4}
Is this relation a
function?
Range: {-8,-4,7,11,13}

27. 6.
x y
0 -2
Example: -2 1
3 -2
-4 4
1 -3

28. 6.
x y
0 -2
Example: -2 1
3 -2
-4 4
1 -3
Domain: {-4,-2,0,1,3}
Is this relation a
Range: {-3,-2,1,4} function?

29. 7.
x y
0 4
Example: -1 4
-1 3
-1 0
5 1

30. 7.
x y
0 4
Example: -1 4
-1 3
-1 0
5 1
Domain {-1,0,5}
Is this relation a
Range {0,1,3,4} function?