Transformations of Functions
Using The Geometer's Sketchpad

There are three types of transformations that can be performed on functions; translations, compressions and reflections. In this exercise, you'll explore those transformations and the effects they create on the graph of the function.

Open the sketch transfunc.gsp. On page one of the sketchbook, Translations, plot the following functions and describe how the original function is altered.

  1. f(x - c) To plot this, choose Graph->Plot New Function. Click on the statement of f(x) in your sketch (not the graph of f(x)), then type x, type -, and click on c in your sketch. Then click OK.

  2. f(x + c) To plot this, just double-click on the equation for f(x-c) and you can edit it, instead of plotting a whole new function.

  3. f(x) + c

  4. f(x) - c

Go to page 2 of the document, Dilations. Plot and describe the following functions:
  1. f(cx)

  2. f(x/c)

  3. cf(x)

  4. (1/c)f(x)

Go to page 3 of the document, Reflections. Plot and describe the following functions:
  1. f(-x)

  2. -f(x)


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