1. Review Preview September 29th, 2016
Give an example of two variables that you believe are related. Example: level of education and annual income.

2. U1D1: Relations and Functions

3. Objectives Determine whether a relation represents a function
Determine the domain and range of relations and functions

4. Relation – a relationship between two variables
In the scoring systems of some track meets, for first place you get 5 points, for second place you get 3 points, for third place you get 2 points, and for fourth place you get 1 point. This scoring system is a relation, so it can be shown by 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.

5. Ways to Express Relations
Ordered Pairs
Graph
Mapping Diagram
{(1,3) , (2,4) , (3, 5)}
Mapping x y 1 3 2 4 3 5

6. 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 {5, 3, 2, 1}.

7. Give the domain and range of the relation.x y 1 2 6 5 –4 –1
Domain:
Range:

8. Determining if a relation is a function
A relation is a function if each input has only one output

9. Determine whether these relations represent a function and state the domain and range
B) 1, 4 , 2, 4 , 3, 5 , (6, 10)
C) −3, 9 , −2, 4 , 0, 0 , 1, 1 , (−3, 8)

10. Determine from the graph if the relations represent a function
Determine from the graph if the relations represent a function. If so, state the domain and range.

11. Determine whether the mapping diagram represents a function and state the domain and range.
Level of Education
Unemployment Rate
No High School Diploma
High School Graduate
Some College
College Graduate
8.5%
5.0%
4.2%
2.7%

12. Determine whether the mapping diagram represents a function and state the domain and range.
Carats
Price
0.70
0.71
0.75
0.78
$1529
$1575
$1765
$1798
$1952

13. Practice Problems
pgs : pgs