6 The curve $C$ has equation $\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + 2 \mathrm { x } - 15 } { \mathrm { x } - 2 }$.\\
(a) Find the equations of the asymptotes of $C$.\\

(b) Show that $C$ has no stationary points.\\

(c) Sketch $C$, stating the coordinates of the intersections with the axes.\\
(d) Sketch the curve with equation $\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } - 2 \mathrm { x } - 15 } { \mathrm { x } - 2 } \right|$.\\
(e) Find the set of values of $x$ for which $\left| \frac { 2 x ^ { 2 } + 4 x - 30 } { x - 2 } \right| < 15$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2023 Q6}}