Combining transformations of functions

Combining transformations of functions

Lessons

  • 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

  • 2.
    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:
    a)
    stretching horizontally by a factor of 2 about the y-axis

    b)
    stretching vertically by a factor of 35\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)g(x).


  • 3.
    Use “Coordinate Mapping Formula” to Graph a Transformed Function
    Given the graph of y=f(x)y = f\left( x \right) as shown,
    a)
    describe every step of transformations applied to: y=14f(3x2)1y = \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.
    Combining transformations of functions