Transformations of functions: Horizontal stretches

Transformations of functions: Horizontal stretches

Lessons

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

Teacher pug

Transformations of functions: Horizontal stretches

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