section 5.1a linear functions and graphs. a ________ is a set of __________________. relationordered...
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SECTION 5.1a
Linear Functions and Graphs
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A ________ is a set of __________________.relation ordered pairs
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
The ________ is the ______ of ________ numbers in a relation.
range
set first
The ________ is the ______ of ________ numbers in a relation.
domain
set second
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EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____}
Range: {____ , ___, ____}
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EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____} -3 -2 0 3
Range: {____ , ___, ____}
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EXAMPLE
Relation = { (3,5),(-2,8),(-3,8),(0,-6) }
Domain: { ____, ____, ___, ____}
Range: {____ , ___, ____}
-3 -2 0 3
-6 5 8
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Three other ways to represent a relation:
1. Mapping:
-3-203
-658
Domain Range
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Three other ways to represent a relation:
2. Table:
domai
n rangex y-3
-2
0
3
8
8
-6
5
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Three other ways to represent a relation:
3. Graph:
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Example 1: Represent the following relations as a set of ordered pairs.
-2056
-327
{ }(-2, 2) (0, -3) (5, 7) (6, 7)
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{ }(2,0) (-2,2) (-2,-2) (-6, 2)
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{ }
-3
-1
0
2
4
x y
0
-2
3
-7
4
(-3,0) (-1,-2) (0,3)
(2,-7) (4,4)
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A ___________ is a relation in which no number in the
_________ is __________.
function
domain repeated
Functions can be represented four different ways:
1. ______________
2. ______________
3. ______________
4. ______________
mapping
graph
table
Set of ordered pairs
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Example 2: Represent the following function as a mapping, graph, and table.
{(7,4),(-3,6),(5,8),(4,3),(1,-3)}
-31457
-33468
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{(7,4),(-3,6),(5,8),(4,3),(1,-3)}
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{(7,4),(-3,6),(5,8),(4,3),(1,-3)}
-3
x y
145
7
6-338
4
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Example 3: Are the following relations also functions?
0 -2 3 -7
-4 5
8
0 -2 3 -7
-4 5 8
Each element of the domain is only used
once.
FUNCTION
3 is used twice.
NOT A FUNCTION
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C
Will all vertical lines cross the graph at only one point?
FUNCTION
YES. Each x is only used once.
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D
Will all vertical lines cross the graph at only one point?
FUNCTION
YES. Each x is only used once.
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E
Will all vertical lines cross the graph at only one
point?
NOT A
FUNCTION
NO. x =-3 is used twice.
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F
Will all vertical lines cross the graph at only one
point?
NOT A
FUNCTION
NO. x =-2 is used three times.
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-4
-2
2
-4
x y
0
-3
3
1
Are all x values used only once?
NO. x = - 4 is used twice.
NOT A
FUNCTION