1.12 Transformations of functions: Horizontal stretches

Transformations of functions: Horizontal stretches

Lessons

    • a)
      Sketch the following functions on the same set of coordinate axes:
      y=(x4)2y = {\left( {x - 4} \right)^2} y=(2x4)2y = {\left( {2x - 4} \right)^2} y=(x34)2y = {\left( {\frac{x}{3} - 4} \right)^2}
    • 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 _____________.
    • 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 ______________________.
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Transformations of functions: Horizontal stretches

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