7 Fig. 7 shows an incomplete sketch of \(y = \frac { ( 2 x - 1 ) ( x + 3 ) } { ( x - 3 ) ( x - 2 ) }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e449d411-aaa9-4167-aa9c-c28d31446d52-3_786_1376_450_386}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
- Find the coordinates of the points where the curve cuts the axes.
- Write down the equations of the three asymptotes.
- Determine whether the curve approaches the horizontal asymptote from above or below for large positive values of \(x\), justifying your answer. Copy and complete the sketch.
- Solve the inequality \(\frac { ( 2 x - 1 ) ( x + 3 ) } { ( x - 3 ) ( x - 2 ) } < 2\).