5.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{937edb48-ef4c-4974-a571-60b0fded841b-3_394_680_982_680}
\end{figure}
Figure 1 shows part of the curve with equation \(y = \mathrm { f } ( x ) , x \in \mathbb { R }\). The curve meets the \(x\)-axis at \(P ( p , 0 )\) and meets the \(y\)-axis at \(Q ( 0 , q )\).
- On separate diagrams, sketch the curve with equation
- \(y = | \mathrm { f } ( x ) |\),
- \(y = 3 \mathrm { f } \left( \frac { 1 } { 2 } x \right)\).
In each case show, in terms of \(p\) or \(q\), the coordinates of points at which the curve meets the axes.
Given that \(\mathrm { f } ( x ) = 3 \ln ( 2 x + 3 )\),
- state the exact value of \(q\),
- find the value of \(p\),
- find an equation for the tangent to the curve at \(P\).