Sketch transformations from algebraic function

Questions that give an explicit algebraic function (like f(x) = x³ - 6x² + 5x + 12 or f(x) = ln x) and ask students to sketch the original and/or transformed versions, requiring both algebraic manipulation and transformation application.

4 questions · Moderate -0.7

1.02w Graph transformations: simple transformations of f(x)
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Edexcel C3 2013 June Q2
7 marks Moderate -0.8
2. Given that $$\mathrm { f } ( x ) = \ln x , \quad x > 0$$ sketch on separate axes the graphs of
  1. \(\quad y = \mathrm { f } ( x )\),
  2. \(y = | \mathrm { f } ( x ) |\),
  3. \(y = - \mathrm { f } ( x - 4 )\). Show, on each diagram, the point where the graph meets or crosses the \(x\)-axis. In each case, state the equation of the asymptote.
OCR C1 Q8
9 marks Moderate -0.3
8. $$f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12$$
  1. Show that $$( x + 1 ) ( x - 3 ) ( x - 4 ) \equiv x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12 .$$
  2. Sketch the curve \(y = \mathrm { f } ( x )\), showing the coordinates of any points of intersection with the coordinate axes.
  3. Showing the coordinates of any points of intersection with the coordinate axes, sketch on separate diagrams the curves
    1. \(\quad y = \mathrm { f } ( x + 3 )\),
    2. \(y = \mathrm { f } ( - x )\).
OCR MEI C3 2009 January Q5
8 marks Moderate -0.8
5
  1. State the period of the function \(\mathrm { f } ( x ) = 1 + \cos 2 x\), where \(x\) is in degrees.
  2. State a sequence of two geometrical transformations which maps the curve \(y = \cos x\) onto the curve \(y = \mathrm { f } ( x )\).
  3. Sketch the graph of \(y = \mathrm { f } ( x )\) for \(- 180 ^ { \circ } < x < 180 ^ { \circ }\).
Edexcel C1 Q8
10 marks Moderate -0.8
\(\text{f}(x) = x^3 - 6x^2 + 5x + 12\).
  1. Show that $$(x + 1)(x - 3)(x - 4) \equiv x^3 - 6x^2 + 5x + 12.$$ [3]
  2. Sketch the curve \(y = \text{f}(x)\), showing the coordinates of any points of intersection with the coordinate axes. [3]
  3. Showing the coordinates of any points of intersection with the coordinate axes, sketch on separate diagrams the curves
    1. \(y = \text{f}(x + 3)\),
    2. \(y = \text{f}(-x)\). [4]