1.13 Transformations of functions: Vertical stretches

Transformations of functions: Vertical stretches

Lessons

    • a)
      Sketch the following functions:
      (y)=x2+2\left( y \right) = {x^2} + 2 (2y)=x2+2\left( {2y} \right) = {x^2} + 2 (y3)=x2+2\left( {\frac{y}{3}} \right) = {x^2} + 2
    • b)
      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 ____________.
    • a)
      y=12f(x)y = \frac{1}{2}f\left( x \right)
    • b)
      y=43f(x)y = \frac{4}{3}f\left( x \right)
    • c)
      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 ______________________.
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Transformations of functions: Vertical stretches

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