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SECTION 5.1a Linear Functions and Graphs

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A ________ is a set of __________________. relationordered pairs Relation = { (3,5),(-2,8),(-3,8),(0,-6) } The ________ is the ______ of ________ numbers in a relation. range setfirst The ________ is the ______ of ________ numbers in a relation. domain setsecond

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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: { ____, ____, ___, ____} -3-203 Range: {____, ___, ____}

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EXAMPLE Relation = { (3,5),(-2,8),(-3,8),(0,-6) } Domain: { ____, ____, ___, ____} Range: {____, ___, ____} -3-203 -658

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Three other ways to represent a relation : 1. Mapping: -3 -2 0 3 -6 5 8 DomainRange

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Three other ways to represent a relation : 2. Table: domainrange xy -3 -2 0 3 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. -2 0 5 6 -3 2 7 { } (-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 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 domainrepeated 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)} -3 1 4 5 7 -3 3 4 6 8

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{(7,4),(-3,6),(5,8),(4,3),(1,-3)}

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-3 x y 1 4 5 7 6 3 8 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

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