9. In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-26_595_716_420_662}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = \sqrt { x } \quad x > 0$$
The point \(P ( 9,3 )\) lies on the curve and is shown in Figure 5.
On the next page there is a copy of Figure 5 called Diagram 1.
- On Diagram 1, sketch and clearly label the graphs of
$$y = \mathrm { f } ( 2 x ) \text { and } y = \mathrm { f } ( x ) + 3$$
Show on each graph the coordinates of the point to which \(P\) is transformed.
The graph of \(y = \mathrm { f } ( 2 x )\) meets the graph of \(y = \mathrm { f } ( x ) + 3\) at the point \(Q\).
- Show that the \(x\) coordinate of \(Q\) is the solution of
$$\sqrt { x } = 3 ( \sqrt { 2 } + 1 )$$
- Hence find, in simplest form, the coordinates of \(Q\).
\includegraphics[max width=\textwidth, alt={}]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-27_599_720_274_660}
\section*{Diagram 1}
Turn over for a copy of Diagram 1 if you need to redraw your graphs.
Only use this copy if you need to redraw your graphs.
\includegraphics[max width=\textwidth, alt={}, center]{f1e1d4f5-dd27-4839-a6f3-f6906666302c-29_600_718_1991_660}
Copy of Diagram 1