7 Fig. 7 shows an incomplete sketch of \(y = \frac { c x ^ { 2 } } { ( b x - 1 ) ( x + a ) }\) where \(a , b\) and \(c\) are integers. The asymptotes of the curve are also shown.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{597abea9-6d00-416e-9203-d5bce9bd1af1-3_928_996_493_535}
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\caption{Fig. 7}
\end{figure}
- Determine the values of \(a , b\) and \(c\).
Use these values of \(a , b\) and \(c\) throughout the rest of the question.
- Determine how the curve approaches the horizontal asymptote for large positive values of \(x\), and for large negative values of \(x\), justifying your answer. On the copy of Fig. 7, sketch the rest of the curve.
- Find the \(x\) coordinates of the points on the curve where \(y = 1\). Write down the solution to the inequality \(\frac { c x ^ { 2 } } { ( b x - 1 ) ( x + a ) } < 1\).