Relations and Functions

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Section 1-1

• Relations and Functions

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(1,2), (2,3), (3,4), (4,5)

• Relation any set of ordered pairs
• Abscissa the first coordinate (x) of an ordered
  pair
• Ordinate the second coordinate (y) of an ordered
  pair

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(1,2), (2,3), (3,4), (4,5)

• Domain the set of all possible abscissas or
  x-values
• D 1, 2, 3, 4
• Range the set of all possible ordinates or
  y-values
• R 2, 3, 4, 5

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Functions

• A function is a relation in which each element of
  the domain is paired with exactly one element of
  the range.
• In other wordsall the x-values are different.

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Vertical Line Test

• We can use the vertical line test to test the
  graph of a relation to determine if it is a
  function.
• Try some of these

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Function Notation

• f(x) is function notation for the value of the
  function, f, at x.
• It is read f of x.
• y f(x)
• Ordered pair form (x, y) (x, f(x))

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Examples

• Find the function values for each given x.
• Find the domain of each of the following
  functions.
• Remember, the domain is the set of all possible
  x-values.

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f(x) 2x x2 -2

• Find f(4)
• Find f(0)
• Find f(-3)
• Now find the domain of f.

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f(x) 2x x2 -2

• x2 - 2 0
• x2 2
• x v2
• D all real s, x v2

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f(x) vx-3

• f(4)
• f(12)
• f(3)
• Find the domain.

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f(x) x2 3

• f(2)
• f(-3)
• f(x1)
• Find the domain.

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f(x) xGreatest Integer Function the
greatest integer not larger than x

• f(2.2)
• f(2.0)
• f(2.9)
• f(-5.5)
• f(-5.1)
• f(-6)

f(0.1) f(0.3) f(0.9)
Now graph it!
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Homework

• Page 10
• 6-52 evens, 54-55