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Date May 2009 Marks available 4 Reference code 09M.1.sl.TZ1.5
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 5 Adapted from N/A

Question

Let \(f(x) = {x^2}\) and \(g(x) = 2{(x - 1)^2}\) .

The graph of g can be obtained from the graph of f using two transformations.

Give a full geometric description of each of the two transformations.

[2]
a.

The graph of g is translated by the vector \(\left( {\begin{array}{*{20}{c}}
3\\
{ - 2}
\end{array}} \right)\) to give the graph of h.

The point \(( - 1{\text{, }}1)\) on the graph of f is translated to the point P on the graph of h.

Find the coordinates of P.

[4]
b.

Markscheme

in any order

translated 1 unit to the right     A1     N1

stretched vertically by factor 2     A1     N1

[2 marks]

a.

METHOD 1

finding coordinates of image on g     (A1)(A1)

e.g.  \( - 1 + 1 = 0\) , \(1 \times 2 = 2\) , \(( - 1{\text{, }}1) \to ( - 1 + 1{\text{, }}2 \times 1)\) , \((0{\text{, }}2)\)

P is (3, 0)     A1A1     N4

METHOD 2

\(h(x) = 2{(x - 4)^2} - 2\)     (A1)(A1)

P is \((3{\text{, }}0)\)     A1A1     N4

b.

Examiners report

The translation was often described well as horizontal (or shift) one unit right. There was considerable difficulty describing the vertical stretch as it was often referred to as "stretch by 2" or "amplitude of 2". A full description should include the name (e.g. vertical stretch) and value for full marks. Candidates also had difficulty applying two consecutive transformations to a single point. Often the translations were applied directly to \(( - 1{\text{, }}1)\) instead of first mapping from f to g . A good number of candidates correctly found \(h(x)\), but most could not find P from this function.

a.

The translation was often described well as horizontal (or shift) one unit right. There was considerable difficulty describing the vertical stretch as it was often referred to as "stretch by 2" or "amplitude of 2". A full description should include the name (e.g. vertical stretch) and value for full marks. Candidates also had difficulty applying two consecutive transformations to a single point. Often the translations were applied directly to \(( - 1{\text{, }}1)\) instead of first mapping from f to g . A good number of candidates correctly found \(h(x)\), but most could not find P from this function.

b.

Syllabus sections

Topic 2 - Functions and equations » 2.3 » Transformations of graphs.
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