Transformations of functions: Horizontal stretches

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Intros
Lessons
  1. 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}
  2. Sketch all three quadratic functions on the same set of coordinate axes.
  3. 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 _____________.
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Examples
Lessons
  1. Horizontal Stretches
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    1. y=f(2x)y = f\left( {2x} \right)
    2. y=f(13x)y = f\left( {\frac{1}{3}x} \right)
    3. 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