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Transformations of Graphs - Translations, Reflections and Scalings of Graphs

Transformations of Graphs - Translations, Reflections and Scalings of Graphs

The diagram shows the curve \(y = f(x)\) which crosses the axes at coordinates \((0, 4)\) and \((5, 0)\).

Sketch on separate diagrams and, as far as possible, show the coordinates of the points of intersection with the axes for the graphs of

  1. \(y = 2f(x)\),
  2. \(y = -f(x)\),
  3. \(y = f(x + 3)\),
  4. \(y = f\left(\frac{1}{2}x\right)\).

Solution:

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Answer:(a) Intercepts \((5,0),(0,8)\). (b) \((5,0),(0,-4)\). (c) \((2,0),(0,f(3))\), with \(f(3)\) not numerically determined. (d) \((10,0),(0,4)\). All four sketches shown.

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