Pg 133

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Pg 133

• Transformations

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Transformations

• A Transformation is a SHIFT, REFLECTION, OR
  STRETCH/COMPRESSION on a Parent Function
• Translation (h or k)
• Shift, Horizontal or Vertical, that preserves
  size and shape

• Reflection
• - It is a Flip, Horizontal or Vertical,
  over a horizontal or vertical axis that
  preserves size and shape

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Transformations

• Stretch/Compression
• Stretches and Compressions distort,
• or changes the shape and size
• Vertical a (behavior is normal)
• a gt 1 Vertical Stretch
• Described as a Vertical Stretch by a factor of
  a
• 0 lt a lt 1 Vertical Compression
• Described as a Vertical Compression by a factor
  of a
• Horizontal b (Crazy House Opposite)
• b gt 1 Horizontal Compression
• Described as a Horizontal Compression by a factor
  of
• 0 lt b lt 1 Horizontal Stretch
• Described as a Horizontal Stretch by a factor of

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Parent Functions
Whats left if we get rid of all the
Transformations?
A Parent Function is the original function,
before all the transformations were applied
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Vertex FormulaContains the Vertex (h,k)
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Crazy House (Horizontal)
(-) Vertical Reflection
Horizontal Stretch or Compression
Vertical Translation
Vertical Stretch or Compression
(-) Horizontal Reflection
Horizontal Translation
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• Transformations on this function?
• First we must factor inside the parentheses
• Vertical
• (-) Vertical Reflection
• (2/3) Vertical Compression by (2/3)
• (-3) Vertical Translation Down (3)
• Horizontal
• (-) Horizontal Reflection
• (1/2) Horizontal Stretch by (2)
• (-4) Horizontal Translation Right (4)

The Parent function is f(x) x2
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Here is my Parent Functionand My Translated
Function
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Parent Functions
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1. g(x) 5x2 3 _________________________________
   __________
2. g(x) 2(x4)2 ________________________________
   __________
3. g(x) 1/2x2 6 ________________________________
   __________
4. g(x) ( 1/3x)2 5 _____________________________
   ______________
5. g(x) 3(x 8)2 1 _________________________
   __________________
6. g(x) 7(x 3)2 4 ____________________________
   _______________
7. g(x) ( 2x)2 3 ______________________________
   _____________
8. g(x) ¼ x2 6 _________________________________
   __________