14.1 Transformations of functions: Horizontal translations

Transformations of functions: Horizontal translations

Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x –h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the right.

Lessons

    • a)
      Sketch the following functions on the same set of coordinate axes:
      y=(x)2y = {\left( x \right)^2}      VS.      y=(x6)2y = {\left( {x - 6} \right)^2}      VS.      y=(x+5)2y = {\left( {x + 5} \right)^2}
    • b)
      Compared to the graph of y=x2y = {x^2}:
      • the graph of y=(x6)2y = {\left( {x - 6} \right)^2} is translated "horizontally" ________ units to the ______________.
      • the graph of y=(x+5)2y = {\left( {x + 5} \right)^2} is translated "horizontally" ________ units to the ______________.
    • a)
      y=f(x8)y = f\left( {x-8} \right)
    • b)
      y=f(x+3)y = f\left( {x+3} \right)
    • c)
      In conclusion:
      (x)(x8)\left( x \right) \to \left( {x-8} \right): shift __________ to the __________. All x coordinates ? ____________________
      (x)(x+3)\left( x \right) \to \left( {x+3} \right): shift __________ to the __________. All x coordinates ? ____________________
Teacher pug

Transformations of functions: Horizontal translations

Don't just watch, practice makes perfect.

We have over 2670 practice questions in Algebra 2 for you to master.