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:
   $y = - 2f\left[ {3\left( {x + 4} \right)} \right] + 5$
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:
   1. stretching horizontally by a factor of 2 about the y-axis
   2. stretching vertically by a factor of $\frac{3}{5}$ about the x-axis
   3. vertical translation of 7 units up
   4. reflection in the y-axis
   5. horizontal translation of 4 units to the left
   6. reflection in the x-axis
      
      Write the function for $g(x)$.
3. Use "Coordinate Mapping Formula" to Graph a Transformed Function
   Given the graph of $y = f\left( x \right)$ as shown,
   1. describe every step of transformations applied to: $y = \frac{1}{4}f\left( {3 - \frac{x}{2}} \right) - 1$
   2. Graph the transformed function on the same set of coordinate axes.
   3. Shortcut: use "Coordinate Mapping Formula" to graph the transformed function.