Graphing transformations of exponential functions

Lessons

• 1.
  Horizontal Translation of an Exponential Function
  Sketch and compare the graphs of the exponential function $y=2^x$ and
  i)

  $y=2^{(x+1)}$
  ii)

  $y=2^{(x-2)}$
  
  Did the transformation affect the horizontal asymptote?

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• 2.
  Vertical Translation of an Exponential Function
  Sketch and compare the graphs of the exponential function $y=2^x$ and
  i)

  $y=2^x+1$
  ii)

  $y=2^x-2$
  
  Did the transformation affect the horizontal asymptote?

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• 3.
  Expansion/Compression of an Exponential Function
  Sketch and compare the graphs of the exponential function $y=2^x$ and
  i)

  $y=2^{3x}$ and $y=2^{\frac{1}{2}x}$
  ii)

  $y=3 \cdot 2^x$ and $y=\frac{1}{2} \cdot 2^x$
  
  

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• 4.
  Reflection of an Exponential Function
  Sketch and compare the graphs of the exponential function $y=2^x$ and
  i)

  $y=2^{-x}$
  ii)

  $y=-2^x$
  
  

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• 5.
  Multiple Transformation
  Compare to $y=2^x$,
  i)

  Describe the transformations involved in $y=6 \cdot 2^{(x+1)}-3$.
  ii)

  Sketch both exponential functions on the same graph.
  iii)

  For $y=6 \cdot 2^{(x+1)}-3$, state its
  

  - asymptote
  

  - domain
  

  - range
  

  - x-intercept
  

  - y-intercept
  

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• 6.
  Compare to $y=2^x$,
  i)

  Describe the transformations involved in $y=-3 \cdot 2^{(x-2)}+6$.
  ii)

  Sketch both exponential functions on the same graph.
  iii)

  For $y=-3 \cdot 2^{(x-2)}+6$, state its
  

  - asymptote
  

  - domain
  

  - range
  

  - x-intercept
  

  - y-intercept
  

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