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2.1Relations and Functions
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What is a Relation?• A relation is a set of pairs of inputs and
outputs.
• They can be written as an ordered pair
• They can be graphed
• They can be expressed in a mapping diagram
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Ordered Pairs
• 0, 1, 2, 5 are all considered “inputs”
• These are all the “x” coordinates
• 5, 7, 6, 0 are all considered “outputs”
• These are all the “y” coordinates
)}0,5(),6,2(),7,1(),5,0{(
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Graph )}0,5(),6,2(),7,1(),5,0{(
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Mapping Diagram)}0,5(),6,2(),7,1(),5,0{(
INPUT OUTPUT
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Create a mapping diagram
)}2,4(),12,7(),1,5(),9,2(),3,1{(
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Domain
• Set of all inputs of a relation
• The “x” coordinate
Range
• The set of all outputs of a relation
• The “y” coordinate
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Example
Find the domain and range of the relation
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Functions• A function is defined as a relation in which
every input (element in the domain) is paired with exactly one output (element in the range).
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Mapping diagrams
1
2
4
5
7
-2
1
3
9
12
Every input mapped to exactly one output-this is a function.
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Mapping diagrams
1
2
4
5
-2
1
3
9
12
7 is mapped to TWO outputs-NOT a function
7
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Graphing
• The vertical line test is used when determining if a graph of a relation is a function.
• If we can draw a vertical line through every part of the graph and have it only go through ONE point, then the relation is a function.
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Graph
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Graph
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Ordered Pairs
• When looking at ordered pairs to determine if they represent a function, there can be no repeating x’s.
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Ordered Pairs-Determine if they represent a function
)}2,7(),1,9(),2,3(),1,0{(
)}2,0(),9,4(),2,3(),1,0{(
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Function notation
• When using function notation, we use F(x) instead of y
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How to work with function notation
For each function, find f(3), f(1) and f(9)
92)( xxf 12)( 2 xxf
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Homework
8/29: #6 pg 42 1,2,6-21, 24-378/30: #7 pg 534 2-28 even, 36-40 all8/31: QUIZ 1.3-9.79/1: #8 pg 59 2-44 even, 46-48 all, 50-54 even, 56 (use a table to graph)