| Date | May 2013 | Marks available | 3 | Reference code | 13M.2.sl.TZ1.6 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Write down | Question number | 6 | Adapted from | N/A |
Question
Let \(f\) and \(g\) be functions such that \(g(x) = 2f(x + 1) + 5\) .
(a) The graph of \(f\) is mapped to the graph of \(g\) under the following transformations:
vertical stretch by a factor of \(k\) , followed by a translation \(\left( \begin{array}{l}
p\\
q
\end{array} \right)\) .
Write down the value of
(i) \(k\) ;
(ii) \(p\) ;
(iii) \(q\) .
(b) Let \(h(x) = - g(3x)\) . The point A(\(6\), \(5\)) on the graph of \(g\) is mapped to the point \({\rm{A}}'\) on the graph of \(h\) . Find \({\rm{A}}'\) .
The graph of \(f\) is mapped to the graph of \(g\) under the following transformations:
vertical stretch by a factor of \(k\) , followed by a translation \(\left( \begin{array}{l}
p\\
q
\end{array} \right)\) .
Write down the value of
(i) \(k\) ;
(ii) \(p\) ;
(iii) \(q\) .
Let \(h(x) = - g(3x)\) . The point A(\(6\), \(5\)) on the graph of \(g\) is mapped to the point \({\rm{A}}'\) on the graph of \(h\) . Find \({\rm{A}}'\) .
Markscheme
(a) (i) \(k = 2\) A1 N1
(ii) \(p = - 1\) A1 N1
(iii) \(q = 5\) A1 N1
[3 marks]
(b) recognizing one transformation (M1)
eg horizontal stretch by \(\frac{1}{3}\) , reflection in \(x\)-axis
\({\rm{A'}}\) is (\(2\), \( - 5\)) A1A1 N3
[3 marks]
Total [6 marks]
(i) \(k = 2\) A1 N1
(ii) \(p = - 1\) A1 N1
(iii) \(q = 5\) A1 N1
[3 marks]
recognizing one transformation (M1)
eg horizontal stretch by \(\frac{1}{3}\) , reflection in \(x\)-axis
\({\rm{A'}}\) is (\(2\), \( - 5\)) A1A1 N3
[3 marks]
Total [6 marks]
Examiners report
Part (a) was frequently done well but a lack of understanding of the notation \(f (x +1)\) often led to an incorrect value for \(p\). In part (b), candidates did not recognize the simplicity of the problem. Most seemed to be unable to correctly recognize the two transformations implied in the question and were thus unable to attempt a geometric solution. Flawed algebraic approaches to part (b) were common and many could not interpret the notation \(g(3x)\) as multiplying the \(x\)-value by \(\frac{1}{3}\).
Part (a) was frequently done well but a lack of understanding of the notation \(f (x +1)\) often led to an incorrect value for \(p\). In part (b), candidates did not recognize the simplicity of the problem. Most seemed to be unable to correctly recognize the two transformations implied in the question and were thus unable to attempt a geometric solution. Flawed algebraic approaches to part (b) were common and many could not interpret the notation \(g(3x)\) as multiplying the \(x\)-value by \(\frac{1}{3}\).
Part (a) was frequently done well but a lack of understanding of the notation \(f (x +1)\) often led to an incorrect value for \(p\). In part (b), candidates did not recognize the simplicity of the problem. Most seemed to be unable to correctly recognize the two transformations implied in the question and were thus unable to attempt a geometric solution. Flawed algebraic approaches to part (b) were common and many could not interpret the notation \(g(3x)\) as multiplying the \(x\)-value by \(\frac{1}{3}\).
