2.1 relations and functions. what is a relation? a relation is a set of pairs of inputs and outputs....

2.1Relations and Functions

What is a Relation?• A relation is a set of pairs of inputs and

outputs.

• They can be written as an ordered pair

• They can be graphed

• They can be expressed in a mapping diagram

Ordered Pairs

• 0, 1, 2, 5 are all considered “inputs”

• These are all the “x” coordinates

• 5, 7, 6, 0 are all considered “outputs”

• These are all the “y” coordinates

)}0,5(),6,2(),7,1(),5,0{(

Graph )}0,5(),6,2(),7,1(),5,0{(

Mapping Diagram)}0,5(),6,2(),7,1(),5,0{(

INPUT OUTPUT

Create a mapping diagram

)}2,4(),12,7(),1,5(),9,2(),3,1{(

Domain

• Set of all inputs of a relation

• The “x” coordinate

Range

• The set of all outputs of a relation

• The “y” coordinate

Example

Find the domain and range of the relation

Functions• A function is defined as a relation in which

every input (element in the domain) is paired with exactly one output (element in the range).

Mapping diagrams

1

2

4

5

7

-2

1

3

9

12

Every input mapped to exactly one output-this is a function.

Mapping diagrams

1

2

4

5

-2

1

3

9

12

7 is mapped to TWO outputs-NOT a function

7

Graphing

• The vertical line test is used when determining if a graph of a relation is a function.

• If we can draw a vertical line through every part of the graph and have it only go through ONE point, then the relation is a function.

Graph

Graph

Ordered Pairs

• When looking at ordered pairs to determine if they represent a function, there can be no repeating x’s.

Ordered Pairs-Determine if they represent a function

)}2,7(),1,9(),2,3(),1,0{(

)}2,0(),9,4(),2,3(),1,0{(

Function notation

• When using function notation, we use F(x) instead of y

How to work with function notation

For each function, find f(3), f(1) and f(9)

92)( xxf 12)( 2 xxf

Homework

8/29: #6 pg 42 1,2,6-21, 24-378/30: #7 pg 534 2-28 even, 36-40 all8/31: QUIZ 1.3-9.79/1: #8 pg 59 2-44 even, 46-48 all, 50-54 even, 56 (use a table to graph)