Transformations of functions: Vertical stretches

Transformations of functions: Vertical stretches

Lessons

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

    a)
    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 ____________.


  • 1.
    Vertical Stretches
    Given the graph of y=f(x)y = f\left( x \right) as shown, sketch:
    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 ______________________.
    Vertical stretches in transformations