Name_______________________________________ Date Watched___________________
Unit 5 PART 1 – Relations and Functions
Lesson 3 – Deciding Relation or Function for Ordered Pairs, Tables, and Mapping Diagrams
Essential Questions:
1. What are relations and functions?
2. Given a relationship’s ordered pairs, table, or mapping diagram, how can I decide if it is a relation or
a function?
Let’s Review:


What is a relation?
A relation is just a ______________________________________________________________
_____________________________________________________________________________
What is a function?
A function is a ________________________________________________________________
_____________________________________________________________________________
Deciding Relation or Function if the relationship is shown as a…
Set of Points
Table
Mapping Diagram
Example:
Example:
Example:
Deciding Relation or Function, if the relationship is shown as a set of points:
Example: In the scoring system of some track meets, for first place a runner gets 5 points, for second
place, a runner gets 3 points, for third place, a runner gets 2 points, and for fourth place, a runner gets 1
point.

This scoring system is a relationship between _____________________________ and
________________________________________.

This scoring system between place and points can be represented by the set of ordered pairs:
_________________________________________________________________________

Is this a relation or a function? (Does each input have one and only one output?)
Examples: Decide relation or function for the given set of points.
{(6,-1), (5,0), (2,-4), (1,0)}
{(1,1), (4,4), (2,8), (1,6)}
{(9,8), (12,-2), (3,14), (9,3), (8,14)}
{(-3,4), (-2,5), (-1,6), (0,7), (1,6), (2,5)}
Benefits & Drawbacks to deciding with a set of points.
Benefits:

Organizes the relationship
__________________________________
Drawbacks:

Many relationships have many possible inputs
and outputs and not all of them can be listed
in a reasonable way.
Deciding Relation or Function, if the relationship is shown as a table.

A table is another way of writing the ordered pairs.
Example: Buses needed for a field trip:
Example: You can burn 6 calories per minute.
Input
(Student)
Output
(Buses)
Input
(Student)
Output
(Buses)
25
1
1
6
45
2
2
12
65
2
3
18
85
3
4
24
105
3
5
30
More Examples: Decide relation or function for each given table.
Input
Output
Input
Output
3
9
2
1
5
25
2
½
2
4
3
2
8
64
3
1½
6
36
4
3
Input
Output
Input
Output
4
0
-1
1
0
4
-3
3
2
2
5
-5
0
-4
-7
7
-4
0
3
-3
Benefits & Drawbacks to deciding with a table.
Benefits:


Organizes the relationship numerically.
Clearly ________________ inputs and
outputs.
Drawbacks:

Since a relationship can have many different
inputs and outputs, a table may get very
____________________ depending on the
number of relationships shown.
Deciding Relation or Function, if the relationship is shown as a mapping diagram:

A mapping diagram tells you ____________________________________________________.
Example: Track Meet Scoring System: {(1,5), (2,3), (3,2), (4,1)}
Examples: Decide relation or function for each given mapping diagram.
{(6,-1), (5,0), (2,-4), (1,0)}
{(1,1), (4,4), (2,8), (1,6)}
{(1,8), (4,6), (7, 5), (3,9), (1,3)}
Benefits & Drawbacks to deciding with a mapping diagram.
Benefits:



Organizes the relationship numerically.

Separates inputs and outputs.
Clearly marks whether an input has ______ or
___________________ output.
Drawbacks:
It can be difficult to tell the number or
numbers an input outputs if there are a lot of
lines drawn on the mapping diagram.
Summarize – Relation or Function
Set of Points
Table
{(2,1), (6,4), (3,8)}
Mapping Diagram
Input
Output
2
1
6
4
3
8
Function if…
Function if…
Function if…
__________________________
__________________________
__________________________
__________________________
__________________________
__________________________
Relation if…
Relation if…
Relation if…
__________________________
__________________________
__________________________
__________________________
__________________________
__________________________
Reflection Questions:
1. Do you understand that relations merely state that a relationship exists?
yes
or
no
2. Do you understand that a function is a consistent, reliable, and predicable relationship in which
each input has one and only one output?
yes
or
no
3. Can you decide if a set of points is a relation or function?
yes
or
no
4. Can you decide if a table is a relation or function?
yes
or
no
5. Can you decide if a mapping diagram is a relation or function?
yes
or
no
6. Do you want to meet with Mrs. Daniel during study hall about this lesson? yes
or
no
Practice Problems: Decide if each is a relation or a function.
{(3, 1), (5, 2), (7, 3), (9, 4)}
Input Output
2
-4
1
-2
0
0
-1
-2