14.2 Transformations of functions: Vertical translations

Transformations of functions: Vertical translations

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 horizontal shift. If h > 0, then the graph shifts h units up; while If h < 0, then the graph shifts h units down.

Lessons

    • a)
      Sketch the following functions on the same set of coordinate axes:
      (y)=x2\left( y \right) = {x^2}, (y3)=x2\left( {y - 3} \right) = {x^2}, (y+2)=x2\left( {y + 2} \right) = {x^2}
    • b)
      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 _____________.
    • a)
      y=f(x)8y = f\left( x \right) - 8
    • b)
      y=f(x)+3y = f\left( x \right) + 3
    • c)
      In conclusion:
      (y)(y+8)\left( y \right) \to \left( {y + 8} \right): shift ________ units ______________ ? all yy coordinates _____________________________.
      (y)(y3)\left( y \right) \to \left( {y - 3} \right): shift ________ units ______________ ? all yy coordinates _____________________________.
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Transformations of functions: Vertical translations

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