14 The function f is defined by
$$\mathrm { f } ( x ) = \frac { x ^ { 2 } - 3 } { x ^ { 2 } + p x + 7 } \quad x \in \mathbb { R }$$
where \(p\) is a constant.
The graph of \(y = \mathrm { f } ( x )\) has only one asymptote.
14
- Write down the equation of the asymptote.
14 - Find the set of possible values of \(p\)
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14 - Find the coordinates of the points at which the graph of \(y = \mathrm { f } ( x )\) intersects the axes.
\section*{Question 14 continues on the next page}
14
- \(\quad A\) curve \(C\) has equation
$$y = \frac { x ^ { 2 } - 3 } { x ^ { 2 } - 3 x + 7 }$$
The curve \(C\) has a local minimum at the point \(M\) as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{fd9715c4-9ce1-4608-aed6-f3d4f71208b5-24_371_835_587_605}
The line \(y = k\) intersects curve \(C\)
14 - Show that
$$19 k ^ { 2 } - 16 k - 12 \leq 0$$
14
- (ii) Hence, find the \(y\)-coordinate of point \(M\)