Honors Precalculus

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Honors Precalculus

• Chapter 1

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• Relation pairs of quantities that have a
  relationship
• Function all domain values (x) must be different

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Is the equation a function?

• Slove for y
• NO

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Functions

• Domain x values
• left to right
• Range y values
• low to high

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• Independent x, domain value
• Dependant y, range value

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Domain

• Graph -
• Points -
• Function see domain rules

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Domain Rules

• Polynomial -
• Rational function -
• Even radical -
• Odd radical -

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Piece-wise function

• Example 4

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Difference Quotient
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Library of Functions

• Line
• Absolute Value

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Library of functions

• Radical function
• Quadratic function

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Section 1.3
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Is it a function?

• Graph
• Points
• Equation

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Relative Extrema

• Relative max
• Relative min

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Even and Odd Functions

• Even
• Odd

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Even/Odd Graphs

• Even symmetry in y-axis
• Odd symmetry in origin

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p. 40 83

• Write the height h of the rectangle as a function
  of x

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Section 1.4

• Vertical and Horizontal shifts
• Blue box p. 43
• Reflections
• Blue box p. 45
• Stretch and shrink
• Nonrigid transformations p. 47

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Library of Functions

• Cubic function

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Practice

• P. 49 27-32
• P.49 15-26 on board

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Section 1.5

• Combinations of Functions

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Composite functions

• Domain - Restrict the outputs of g so that they
  are in the domain of f
• Find the domain of g
• Find the domain of the composite
• Overlap

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Class problems p. 59

• 51 54
• 55 60
• 63 65

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Section 1.6 Inverse Functions

• Inverse notation

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Definition of Inverse function

• f(g(x)) x and g(f(x)) x

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Graph of an Inverse

• Inverse functions are reflected in the line y x

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Does a function have an inverse?

• Must be one-to-one
• No two elements in the domain correspond to the
  same element in the range
• Must pass the horizontal line test

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Find the inverse of a function

• Horizontal line test
• Switch x and y
• Solve for y
• Write in function notation

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