Combining transformations of functions

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  1. Describe the Combination of Transformations
    Compared to y=f(x)y = f\left( x \right), describe every step of transformations applied to:
    y=2f[3(x+4)]+5y = - 2f\left[ {3\left( {x + 4} \right)} \right] + 5
    1. Write the Equation of a Transformed Function
      Transform the function f(x)=1xf\left( x \right) = \frac{1}{x} into the function g(x)g\left( x \right) by:
      1. stretching horizontally by a factor of 2 about the y-axis
      2. stretching vertically by a factor of 35\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)g(x).
    2. Use "Coordinate Mapping Formula" to Graph a Transformed Function
      Given the graph of y=f(x)y = f\left( x \right) as shown,
      1. describe every step of transformations applied to: y=14f(3x2)1y = \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.
        Combining transformations of functions