Combining transformations of functions

Lessons

• 1.
  Describe the Combination of Transformations
  Compared to $y = f\left( x \right)$, describe every step of transformations applied to:
  $y = - 2f\left[ {3\left( {x + 4} \right)} \right] + 5$

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• 2.
  Write the Equation of a Transformed Function
  Transform the function $f\left( x \right) = \frac{1}{x}$ into the function $g\left( x \right)$ by:
  a)

  stretching horizontally by a factor of 2 about the y-axis
  
  
  b)

  stretching vertically by a factor of $\frac{3}{5}$ about the x-axis
  
  
  c)

  vertical translation of 7 units up
  
  
  d)

  reflection in the y-axis
  
  
  e)

  horizontal translation of 4 units to the left
  
  
  f)

  reflection in the x-axis
  
  Write the function for $g(x)$.
  
  

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• 3.
  Use "Coordinate Mapping Formula" to Graph a Transformed Function
  Given the graph of $y = f\left( x \right)$ as shown,
  a)

  describe every step of transformations applied to: $y = \frac{1}{4}f\left( {3 - \frac{x}{2}} \right) - 1$
  
  
  b)

  Graph the transformed function on the same set of coordinate axes.
  
  
  c)

  Shortcut: use "Coordinate Mapping Formula" to graph the transformed function.
  
  
  

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