Transformations of functions: Vertical translations

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  1. An Experiment to Study "Vertical Translations"

    Sketch and compare: (y)=x2\left( y \right) = {x^2}
    (y3)=x2\left( {y - 3} \right) = {x^2}
    (y+2)=x2\left( {y + 2} \right) = {x^2}
  2. Sketch all three quadratic functions on the same set of coordinate axes.
  3. Compared to the graph of y=x2y = {x^2}:
    • the graph of (y3)=x2\left( {y - 3} \right) = {x^2} is translated "vertically" ________ units _____________.
    • the graph of (y+2)=x2\left( {y + 2} \right) = {x^2} is translated "vertically" ________ units _____________.
  1. Vertical Translations
    Given the graph of y=f(x)y=f(x) as shown, sketch:
    1. y=f(x)8y = f\left( x \right) - 8
    2. y=f(x)+3y = f\left( x \right) + 3
    3. In conclusion:
      (y)(y+8)\left( y \right) \to \left( {y + 8} \right): shift ________ units ______________ \Rightarrow all yy coordinates _____________________________.
      (y)(y3)\left( y \right) \to \left( {y - 3} \right): shift ________ units ______________ \Rightarrow all yy coordinates _____________________________.
      Vertical translations
Topic Notes
Vertical translations refer to movements of a graph of a function vertically along the y-axis by changing the y values. So, if y = f(x), then y = (x) + h results in a vertical shift. If h > 0, then the graph shifts h units up; while If h < 0, then the graph shifts h units down.