Transformations of functions: Vertical stretches

Lessons

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

  VS.

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

  VS.

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

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

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

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

  $y = \frac{1}{2}f\left( x \right)$
  
  
  b)

  $y = \frac{4}{3}f\left( x \right)$
  
  
  c)

  In conclusion:
  • $\left( y \right) \to \left( {2y} \right)$: vertical stretch by a factor of ________ ⇒ all $y$ coordinates ______________________.
  • $\left( y \right) \to \left( {\frac{3}{4}y} \right)$: vertical stretch by a factor of ________ ⇒ all $y$ coordinates ______________________.
  
  
  

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