8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-16_647_970_306_488}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
The curve \(C\) with equation \(y = \mathrm { f } ( x )\) is shown in Figure 4.
The curve \(C\)
- has a single turning point, a maximum at ( 4,9 )
- crosses the coordinate axes at only two places, \(( - 3,0 )\) and \(( 0,6 )\)
- has a single asymptote with equation \(y = 4\)
as shown in Figure 4.
- State the equation of the asymptote to the curve with equation \(y = \mathrm { f } ( - x )\).
- State the coordinates of the turning point on the curve with equation \(y = \mathrm { f } \left( \frac { 1 } { 4 } x \right)\).
Given that the line with equation \(y = k\), where \(k\) is a constant, intersects \(C\) at exactly one point,
state the possible values for \(k\).
The curve \(C\) is transformed to a new curve that passes through the origin.- Given that the new curve has equation \(y = \mathrm { f } ( x ) - a\), state the value of the constant \(a\).
- Write down an equation for another single transformation of \(C\) that also passes through the origin.