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How to Describe Transformations of Functions

Once a function is graphed properly on a computer, graphing calculator or a simple sheet of graph paper the behavior of that function becomes dramatically clearer to the student. Many functions tend to repeat in a discernible way or are symmetrical. These characteristics can only be understood properly if they are visualized. Describing transformations of functions involves describing the visual changes to the graph of the function that occur when a function is transformed in different ways.

Instructions

    • 1

      Describe a horizontal translation as the shifting of the entire graph of the function side to side as if it were on a train track. You can describe a vertical translation similarly as if the graph of the function was moving up and down like a flag on a flagpole.

    • 2

      Describe a change in amplitude as a stretching or compressing of the graph of the function as if the function were a springy toy that you could either stretch upwards or compress downwards. You can describe a change in scale similarly as if the springy toy were oriented horizontally this time so it could be either stretched wider or compressed tighter.

    • 3

      Describe a reflection of the graph as if it were a mirror, in which your left hand looks like your right hand and vice versa. When you change the sign of the x factor, this puts a mirror on the y axis and vice versa if you change the sign of the y factor.

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