Transformations of functions: Horizontal stretches

Lessons

• Introduction
  An Experiment to Study “Horizontal Stretches”
  Sketch and compare: $y = {\left( {x - 4} \right)^2}$

  VS.

  $y = {\left( {2x - 4} \right)^2}$

  VS.

  $y = {\left( {\frac{x}{3} - 4} \right)^2}$
  a)

  Sketch all three quadratic functions on the same set of coordinate axes.
  
  
  b)

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

---

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

  $y = f\left( {2x} \right)$
  
  
  b)

  $y = f\left( {\frac{1}{3}x} \right)$
  
  
  c)

  In conclusion:
  • $\left( x \right) \to \left( {2x} \right)$: horizontal stretch by a factor of ________ ⇒ all $x$ coordinates ______________________.
  • $\left( x \right) \to \left( {\frac{1}{3}x} \right)$: horizontal stretch by a factor of ________ ⇒ all $x$ coordinates ______________________.
  
  
  

---