Transformations of functions: Horizontal translations

Lessons

• 1.
  a)

  Sketch the following functions on the same set of coordinate axes:
  $y = {\left( x \right)^2}$      VS.      $y = {\left( {x - 6} \right)^2}$      VS.      $y = {\left( {x + 5} \right)^2}$
  
  
  b)

  Compared to the graph of $y = {x^2}$:
  • the graph of $y = {\left( {x - 6} \right)^2}$ is translated "horizontally" ________ units to the ______________.
  • the graph of $y = {\left( {x + 5} \right)^2}$ is translated "horizontally" ________ units to the ______________.
  
  

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• 2.
  Horizontal Translations
  Given the graph of $y = f\left( x \right)$ as shown, sketch:
  a)

  $y = f\left( {x-8} \right)$
  
  
  b)

  $y = f\left( {x+3} \right)$
  
  
  c)

  In conclusion:
  • $\left( x \right) \to \left( {x-8} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________
  • $\left( x \right) \to \left( {x+3} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________
  
  
  

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