Power Functions and Modeling

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Power Functions and Modeling

• 2.2

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Power Function

• Any function that can be written in the form f(x)
  kxa, where k is a non-zero constant and real
  numbers.
• Is a power function.
• The constant a is the power, and k is the
  constant of variation. We say f(x) varies as the
  ath power of x or f(x) is proportional to the ath
  power of x.

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Is this a power function?

• Examples--2-10 even

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Monomial Function

• Any function that can be written as
• F(x) k or f(x) kxn
• Where k is a constant and n is a positive
  integer, is a monomial function.

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Is the function a monomial?

• Examples--12-16 even

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Direct Variation

• Power function with positive powers.
• As x increases, then y increases.
• As your height increases, so does your weight.

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Indirect Variation

• Power function with negative powers.
• As x increases, then y decreases.
• As the speed increases, the time it takes to get
  there decreases.

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Inverse/Direct Variation

• Examples18-26 evens

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Create a power function

• Example--28

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Graphing/Analyzing Power Functions

• Examples 30-40 evens

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The Identity Function

• Domain all reals
• Range all reals
• Continuity yes
• Inc/Dec always increasing
• Symmetry originodd symmetry
• Boundedness unbounded
• Local Extrema none
• Asymptotes none

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The Squaring Function

• Domain all reals
• Range 0, 8)
• Continuity yes
• Inc/Dec increasing on 0, 8), decreasing on
  (-8,0
• Symmetry even symmetry
• Boundedness bounded below
• Local Extrema local min at (0,0)
• Asymptotes none

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The Cubing Function

• Domain all reals
• Range all reals
• Continuity yes
• Inc/Dec always increasing
• Symmetry originodd symmetry
• Boundedness unbounded
• Local Extrema none
• Asymptotes none

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The Square Root Function

• Domain 0, 8)
• Range 0,8)
• Continuity over the domain
• Inc/Dec increasing over the domain
• Symmetry none
• Boundedness bounded below
• Local Extrema local min at (0,0)
• Asymptotes none