4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fa7abe9f-f5c0-4578-afd1-73176c717536-08_755_775_248_662}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve with equation \(y = g ( x )\).
The curve has a single turning point, a minimum, at the point \(M ( 4 , - 1.5 )\).
The curve crosses the \(x\)-axis at two points, \(P ( 2,0 )\) and \(Q ( 7,0 )\).
The curve crosses the \(y\)-axis at a single point \(R ( 0,5 )\).
- State the coordinates of the turning point on the curve with equation \(y = 2 \mathrm {~g} ( x )\).
- State the largest root of the equation
$$g ( x + 1 ) = 0$$
- State the range of values of \(x\) for which \(\mathrm { g } ^ { \prime } ( x ) \leqslant 0\)
Given that the equation \(\mathrm { g } ( x ) + k = 0\), where \(k\) is a constant, has no real roots,
- state the range of possible values for \(k\).