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

  • 1.
    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 _____________.


  • 2.
    Vertical Translations
    Given the graph of y=f(x)y=f(x) as shown, sketch:
    Vertical translations
    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 ______________ \Rightarrow all yy coordinates _____________________________.
    (y)(y3)\left( y \right) \to \left( {y - 3} \right): shift ________ units ______________ \Rightarrow all yy coordinates _____________________________.
    Vertical translations