Algebraic to algebraic transformation description

Questions that give two algebraic function expressions (e.g., y=f(x) to y=2f(x-1) or y=x² to y=4(x-3)²-8) and ask to describe the transformations, without any graphs provided.

7 questions · Moderate -0.9

1.02w Graph transformations: simple transformations of f(x)
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CAIE P1 2021 June Q2
5 marks Moderate -0.8
2
  1. The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 2 \mathrm { f } ( x - 1 )\).
    Describe fully the two single transformations which have been combined to give the resulting transformation.
  2. The curve \(y = \sin 2 x - 5 x\) is reflected in the \(y\)-axis and then stretched by scale factor \(\frac { 1 } { 3 }\) in the \(x\)-direction. Write down the equation of the transformed curve.
CAIE P1 2020 March Q2
4 marks Easy -1.2
2 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 1 + \mathrm { f } \left( \frac { 1 } { 2 } x \right)\).
Describe fully the two single transformations which have been combined to give the resulting transformation.
CAIE P1 2021 November Q1
4 marks Moderate -0.8
1 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 3 - \mathrm { f } ( x )\).
Describe fully, in the correct order, the two transformations that have been combined.
CAIE P1 2020 Specimen Q5
5 marks Moderate -0.8
5
  1. The curve \(y = x ^ { 2 } + 3 x + 4\) is translated by \(\binom { 2 } { 0 }\).
    Find and simplify the equation of the translated curve.
  2. The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 3 \mathrm { f } ( - x )\). Describe fully the two single transformations which have been combined to give the resulting transformation.
Pre-U Pre-U 9794/1 2013 November Q6
Easy -1.3
6 Describe fully the transformations which, when applied to the graph of \(y = \mathrm { f } ( x )\), will produce the graphs with equations given by
  1. \(y = \mathrm { f } ( - x )\),
  2. \(y = \mathrm { f } ( x - 3 )\),
  3. \(y = \mathrm { f } \left( \frac { x } { 2 } \right)\).
OCR MEI Paper 2 Specimen Q2
4 marks Moderate -0.8
Given that \(\text{f}(x) = x^3\) and \(\text{g}(x) = 2x^3 - 1\), describe a sequence of two transformations which maps the curve \(y = \text{f}(x)\) onto the curve \(y = \text{g}(x)\). [4]
SPS SPS SM Pure 2022 June Q8
8 marks Moderate -0.3
The function \(f(x)\) is such that \(f(x) = -x^3 + 2x^2 + kx - 10\) The graph of \(y = f(x)\) crosses the \(x\)-axis at the points with coordinates \((a, 0)\), \((2, 0)\) and \((b, 0)\) where \(a < b\)
  1. Show that \(k = 5\) [1 mark]
  2. Find the exact value of \(a\) and the exact value of \(b\) [3 marks]
  3. The functions \(g(x)\) and \(h(x)\) are such that $$g(x) = x^3 + 2x^2 - 5x - 10$$ $$h(x) = -8x^3 + 8x^2 + 10x - 10$$
    1. Explain how the graph of \(y = f(x)\) can be transformed into the graph of \(y = g(x)\) Fully justify your answer. [2 marks]
    2. Explain how the graph of \(y = f(x)\) can be transformed into the graph of \(y = h(x)\) Fully justify your answer. [2 marks]