7 Fig. 7 shows a sketch of \(y = \frac { x - 4 } { ( x - 5 ) ( x - 8 ) }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2e47c6fb-574b-4eee-81c8-4031fee9e2ba-3_696_975_406_529}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
- Write down the equations of the three asymptotes and the coordinates of the points where the curve crosses the axes. Hence write down the solution of the inequality \(\frac { x - 4 } { ( x - 5 ) ( x - 8 ) } > 0\).
- The equation \(\frac { x - 4 } { ( x - 5 ) ( x - 8 ) } = k\) has no real solutions. Show that \(- 1 < k < - \frac { 1 } { 9 }\). Relate this result to the graph of \(y = \frac { x - 4 } { ( x - 5 ) ( x - 8 ) }\).