Transformations of functions: Vertical stretches

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Intros
Lessons
  1. An Experiment to Study "Vertical Stretches"
    Sketch and compare: (y)=x2+2\left( y \right) = {x^2} + 2
    VS.
    (2y)=x2+2\left( {2y} \right) = {x^2} + 2
    VS.
    (y3)=x2+2\left( {\frac{y}{3}} \right) = {x^2} + 2
  2. a) Sketch all three quadratic functions on the same set of coordinate axes.
  3. Compared to the graph of (y)=x2+2\left( y \right) = {x^2} + 2:
    (2y)=x2+2\left( {2y} \right) = {x^2} + 2 is a vertical stretch about the x-axis by a factor of ____________.
    (y3)=x2+2\left( {\frac{y}{3}} \right) = {x^2} + 2 is a vertical stretch about the x-axis by a factor of ____________.
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Examples
Lessons
  1. Vertical Stretches
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    1. y=12f(x)y = \frac{1}{2}f\left( x \right)
    2. y=43f(x)y = \frac{4}{3}f\left( x \right)
    3. In conclusion:
      (y)(2y)\left( y \right) \to \left( {2y} \right): vertical stretch by a factor of ________ ⇒ all yy coordinates ______________________.
      (y)(34y)\left( y \right) \to \left( {\frac{3}{4}y} \right): vertical stretch by a factor of ________ ⇒ all yy coordinates ______________________.
      Vertical stretches in transformations