5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-12_963_1239_255_354}
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\caption{Figure 1}
\end{figure}
Figure 1 shows the sketch of a curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\).
The curve crosses the \(y\)-axis at \(( 0,4 )\) and crosses the \(x\)-axis at \(( 5,0 )\).
The curve has a single turning point, a maximum, at (2, 7).
The line with equation \(y = 1\) is the only asymptote to the curve.
- State the coordinates of the turning point on the curve with equation \(y = \mathrm { f } ( x - 2 )\).
- State the solution of the equation f( \(2 x\) ) \(= 0\)
- State the equation of the asymptote to the curve with equation \(y = \mathrm { f } ( - x )\).
Given that the line with equation \(y = k\), where \(k\) is a constant, meets the curve \(y = \mathrm { f } ( x )\) at only one point,
- state the set of possible values for \(k\).