| Date | May 2009 | Marks available | 2 | Reference code | 09M.1.sl.TZ1.5 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Give a full geometric description | 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.
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.
Markscheme
in any order
translated 1 unit to the right A1 N1
stretched vertically by factor 2 A1 N1
[2 marks]
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
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.
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.
