how to tell if relations are functions...how to tell if relations are functions 1. graphs: •use...
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3.2_Functions and Relations.notebook
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Aug 910:50 PM
3.2: Relations and Functions
Relations can be represented as the following: set of ordered pairs tablegraph mapping
(1,2)(2,4)(0,3)
x y 12 0
2 43
12 0
2 43
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Relation: Any set of ordered pairs
Function: • A relation where there is only one x for every y • the x's cannot repeat!
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The domain of a relation is the set of first coordinates (or xvalues) of the ordered pairs.
The range of a relation is the set of second coordinates (or yvalues) of the ordered pairs.
Dec 12:52 PM
How to Tell if Relations are Functions
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:• If a mapping has an xvalue with two lines coming from it, it is NOT a function.
4. Ordered Pairs:• If a set of ordered pairs has an x that repeats, then it isn't a function
3.2_Functions and Relations.notebook
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Example 1Express the relations {(3,2), (1,4), (0,3), (3,4), (2,2)} as a table, graph, and mapping.
x yx y
a. What is the domain of the relation? Range?b. Is the relation a function?
Aug 911:17 PM
2356
478
Example 2: Express the relaon as a set of ordered pairs.
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.
Nov 83:24 PM
Example 3: Express the relaon as a set of ordered pairs.
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.
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4. Is the graph a function?
3.2_Functions and Relations.notebook
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5. Is the graph a function?
Nov 62:31 PM
"x" and "y" coordinates in each ordered pair are switched .**The Domain becomes the Range in the inverse.**
RELATION INVERSE RELATION
Inverse Relation
(2,5)(3,2)(6,7)(5,1)
(5,2)(2,3)(7,6)(1,5)
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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 yx y
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.
Nov 61:01 PM
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 yyx
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.
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Example 8:Express the mapping as a set of ordered pairs and as a table. Then write the inverse of the relation.
4079
8235
x y
Set of ordered pairs:
Table: Inverse:
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Example 9:Express the mapping as a set of ordered pairs and as a table. Then write the inverse of the relation.
x y
Set of ordered pairs:
Table: Inverse: