1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4d5b914c-28b2-4485-a42e-627c95fa16e2-02_723_1002_248_584}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where
$$\mathrm { f } ( x ) = 1 + \frac { 4 } { x ( x - 3 ) }$$
The curve has a turning point at the point \(P\), and the lines with equations \(y = 1 , x = 0\) and \(x = a\) are asymptotes to the curve.
- Write down the value of \(a\).
- Find the coordinates of \(P\), justifying your answer.
- Sketch the curve with equation \(y = \left| \mathrm { f } \left( x + \frac { 3 } { 2 } \right) \right| - 1\)
On your sketch, you should show the coordinates of any points of intersection with the coordinate axes, the coordinates of any turning points and the equations of any asymptotes.
\includegraphics[max width=\textwidth, alt={}, center]{4d5b914c-28b2-4485-a42e-627c95fa16e2-02_2255_50_311_1980}