Transformations of functions: Vertical translations

Lessons

• Introduction
  An Experiment to Study “Vertical Translations”
  
  Sketch and compare: $\left( y \right) = {x^2}$

  VS.

  $\left( {y - 3} \right) = {x^2}$

  VS.

  $\left( {y + 2} \right) = {x^2}$
  a)

  Sketch all three quadratic functions on the same set of coordinate axes.
  
  
  b)

  Compared to the graph of $y = {x^2}$:
  • the graph of $\left( {y - 3} \right) = {x^2}$ is translated "vertically" ________ units _____________.
  • the graph of $\left( {y + 2} \right) = {x^2}$ is translated "vertically" ________ units _____________.
  
  

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• 1.
  Vertical Translations
  Given the graph of $y=f(x)$ as shown, sketch:
  a)

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

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

  In conclusion:
  • $\left( y \right) \to \left( {y + 8} \right)$: shift ________ units ______________ $\Rightarrow$ all $y$ coordinates _____________________________.
  • $\left( y \right) \to \left( {y - 3} \right)$: shift ________ units ______________ $\Rightarrow$ all $y$ coordinates _____________________________.
  
  
  

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