Transformations of Graphs - Translations, Reflections and Scalings of Graphs

Transformations of Graphs - Translations, Reflections and Scalings of Graphs

Describe how the graph of \(y = f(x)\) can be transformed to give the graph of

  1. \(y = f(x - 2)\)
  2. \(y = 2f(x)\)
  3. \(y = f(x) - 2\)
  4. \(y = f(2x)\)
  5. \(y = -f(x)\)
  6. \(y = f(-x)\)
  7. \(y = \frac{1}{2}f(x)\)
  8. \(y = f\left(\frac{x}{2}\right)\)

Solution:

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Answer:(a) Right 2. (b) Vertical scale 2. (c) Down 2. (d) Horizontal scale \(\dfrac12\). (e) Reflect in x-axis. (f) Reflect in y-axis. (g) Vertical scale \(\dfrac12\). (h) Horizontal scale 2.

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