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?
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?
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 $y=\frac{1}{2} \cdot 2^x$
   
   
4. Reflection of an Exponential Function
   Sketch and compare the graphs of the exponential function $y=2^x$ and
   i)
   $y=2^{-x}$
   ii)
   $y=-2^x$
   
   
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
   
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