2.2_Functions and Relations.notebook
October 22, 2014
2.2: Relations and Functions
Relations can be represented as the following: set of ordered pairs
(1,2)
(­2,4)
(0,­3)
graph
table
xy
1 2
­2 4
0 ­3
Relation: Any set of ordered pairs
mapping
1
­2
0
2
4
­3
Function: • A relation where there is only one x for every y • the x's cannot repeat!
Example 1
How to Tell if Relations are Functions
Express the relations {(3,2), (­1,4), (0,­3), (­3,4), (­2,­2)} as a table, graph, and mapping.
x
x
y
1. Graphs: • Use the vertical line test
• draw a vertical line through a graph and if it touches the graph in more than one point, it is NOT a function. 2. Tables:
• If a table has an x­value listed twice, it is NOT a function.
• It doesn't matter if the y­values repeat 3. Mappings:
NOT a function.
• If a mapping has an x­value with two lines coming from it, it is 4. Ordered Pairs:
• If a set of ordered pairs has an x that repeats, then it isn't a function
a. What is the domain of the relation? b. Range?
c. Is the relation a function? Explain
y
2.2_Functions and Relations.notebook
October 22, 2014
Example 2: Express the relaon as a set of ordered pairs.
A. What is the domain of the relaon? 2
3
5
6
Example 3: Express the relaon as a set of ordered pairs. ­4
­7
­8
A. What is the domain of the relaon? B. What is the range of the relaon?
B. What is the range of the relaon?
C. Is the relaon a funcon? Explain your answer. C. Is the relaon a funcon? Explain your answer. 4. Is the graph a function?
5. Is the graph a function?
2.2_Functions and Relations.notebook
October 22, 2014
Example 6:
Express the relation {(3,2), (-1,4), (0,-3), (-3,4), and (-2,-2) as a
table, graph, and a mapping. Tell the domain and range.
x
y
x
Inverse Relation
y
"x" and "y" coordinates in each ordered pair are switched .
**The Domain becomes the Range in the inverse.**
RELATION
INVERSE RELATION
(2,5)
(­3,2)
(6,7)
(5,­1)
(5,2)
(2,­3)
(7,6)
(­1,5)
A. What is the domain of the relaon? B. What is the range of the relaon?
C. Is the relaon a funcon? Explain your answer. D. What is the inverse of the relaon as ordered pairs?
E. Is the inverse of the relaon a funcon? Explain your answer. Example 7:
Express the relation {(-1,2), (3,-1), (4,6), (-5,-2) and (1,0)}
as a table, graph and a mapping. Tell the domain and range .
x
x
y
y
Example 8:
Express the mapping as a set of ordered pairs and as a
table. Then write the inverse of the relation.
Set of ordered pairs:
Table:
A. What is the domain of the relaon? B. What is the range of the relaon?
C. Is the relaon a funcon? Explain your answer. D. What is the inverse of the relaon as ordered pairs?
E. Is the inverse of the relaon a funcon? Explain your answer. x
y
Inverse:
­4
0
7
9
­8
­2
3
5
2.2_Functions and Relations.notebook
October 22, 2014
Example 9:
Express the mapping as a set of ordered pairs and as a
table. Then write the inverse of the relation.
Set of ordered pairs:
Table:
x
y
Inverse:
2
3
5
6
­4
­7
­8