Transformations of functions: Horizontal stretches

Transformations of functions: Horizontal stretches

Lessons

  • Introduction
    An Experiment to Study “Horizontal Stretches”
    Sketch and compare: y=(x4)2y = {\left( {x - 4} \right)^2}
    VS.
    y=(2x4)2y = {\left( {2x - 4} \right)^2}
    VS.
    y=(x34)2y = {\left( {\frac{x}{3} - 4} \right)^2}
    a)
    Sketch all three quadratic functions on the same set of coordinate axes.

    b)
    Compared to the graph of y=(x4)2y = {\left( {x - 4} \right)^2}:
    y=(2x4)2y = {\left( {2x - 4} \right)^2} is a horizontal stretch about the y-axis by a factor of _____________.
    y=(x34)2y = {\left( {\frac{x}{3} - 4} \right)^2} is a horizontal stretch about the y-axis by a factor of _____________.


  • 1.
    Horizontal Stretches
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    a)
    y=f(2x)y = f\left( {2x} \right)

    b)
    y=f(13x)y = f\left( {\frac{1}{3}x} \right)

    c)
    In conclusion:
    (x)(2x)\left( x \right) \to \left( {2x} \right): horizontal stretch by a factor of ________ ⇒ all xx coordinates ______________________.
    (x)(13x)\left( x \right) \to \left( {\frac{1}{3}x} \right): horizontal stretch by a factor of ________ ⇒ all xx coordinates ______________________.
    Horizontal stretches in transformations