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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 \({\rm{A}}’\) .
Answer/Explanation
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]