5. (i)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dfb4b2bc-4bc8-4e5b-9b13-ffe4fbde1b4f-14_572_1025_212_463}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\).
The curve passes through the points \(( - 5,0 )\) and \(( 0 , - 3 )\) and touches the \(x\)-axis at the point \(( 2,0 )\).
On separate diagrams sketch the curve with equation
- \(y = \mathrm { f } ( x + 2 )\)
- \(y = \mathrm { f } ( - x )\)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
(ii)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dfb4b2bc-4bc8-4e5b-9b13-ffe4fbde1b4f-14_415_814_1548_571}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the curve with equation
$$y = k \cos \left( x + \frac { \pi } { 6 } \right) \quad 0 \leqslant x \leqslant 2 \pi$$
where \(k\) is a constant.
The curve meets the \(y\)-axis at the point \(( 0 , \sqrt { 3 } )\) and passes through the points \(( p , 0 )\) and ( \(q , 0\) ).
Find - the value of \(k\),
- the exact value of \(p\) and the exact value of \(q\).