11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c32000f-574f-473c-bd04-9cfe2c1bd715-30_630_630_312_721}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the graph with equation
$$y = | 2 x - 3 k |$$
where \(k\) is a positive constant.
- Sketch the graph with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = k - | 2 x - 3 k |$$
stating
- the coordinates of the maximum point
- the coordinates of any points where the graph cuts the coordinate axes
- Find, in terms of \(k\), the set of values of \(x\) for which
$$k - | 2 x - 3 k | > x - k$$
giving your answer in set notation. - Find, in terms of \(k\), the coordinates of the minimum point of the graph with equation
$$y = 3 - 5 f \left( \frac { 1 } { 2 } x \right)$$