Section 8'4 Introduction to Functions

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Section 8.4Introduction to Functions
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Relation

• A relation is a set of ordered pairs of real
  numbers.
• F (3, 2) (4, 1) (2, 4) (1, 3)
• If I say (2, __ ) , can you fill in the blank?
• G (3, 3) (4, 1) (2, 1) (1, 3)
• If I say (4, __ ) , can you fill in the blank?

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DomainF (3, 2) (4, 1) (2, 4) (1, 3)

• In a relation the set of all of the values of the
  independent variable is called the domain.
• What is the domain of F?
• 3, 4, 2, 1
• Does G (3, 3) (4, 1) (2, 1) (1, 3) have the
  same domain?

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Range G (3, 3) (4, 1) (2, 1) (1, 3)

• In a relation the set of all of the values of the
  dependent variable is called the range.
• What is the range of G?
• 3, 1
• Does F (3, 2) (4, 1) (2, 4) (1, 3) have the
  same range?

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(Domain, Range)

• Notice the alphabetical characteristic of Domain
  and Range.
• (x, y)
• (a, b)
• (abscissa, ordinate)
• Unfortunately (independent, dependent) breaks the
  rule.

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Function

• A function is a relation in which , for each
  value of the first component there is exactly one
  value of the second component.
• H (3, 2) (4, 1) (3, 4) (1, 3)
• K (2, 3) (4, 1) (3, 1) (2, 3)
• H is not a function,but K is a function.

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Function Expressed as a Mapping
Domain
Range

• F
• (A,1)
• (C, 2)
• (B, 3)

A
1
C
2
3
B
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Function Expressed as a Mapping
Domain
Range

• G
• (A,1)
• (C, 2)
• (B, 3)
• (A, 4)

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A
1
C
2
3
B
Since A goes to two ranges G is not a function.
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Finding Domains and Ranges from Graphs
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• The range runs from -6 to 6
• -6, 6

The domain runs from -4 to 4 -4, 4
-4
4
-6
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Finding Domains and Ranges from Graphs
The range runs from -? to ? (-?, ?)
The domain runs from - ? to ? (-?, ?)
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Finding Domains and Ranges from Graphs
The range runs from -3 to ? -3, ?)
The domain runs from - ? to ? (-?, ?)
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Vertical Line Test

• If a vertical line intersects the graph of a
  relation in more than one point, then the
  relation is not a function.
• H (3, 2) (4, 1) (3, 4) (1, 3)

Two intersections therefore not a function
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Vertical Line Test
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Vertical Line Test
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Vertical Line Test
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Vertical Line Test
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Vertical Line Test

• Think of the uppercase letters.
  ABCDEFGHIJKLMNOP...
• Which of the uppercase letters would pass the
  vertical line test?

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