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

U1D1: Relations and Functions

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

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.

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

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}.

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

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

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)

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.

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%

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

Practice Problems pgs. 67 - 68: 15 - 26 pgs. 75-76 11-22