- The curve \(y = \mathrm { f } ( x )\) passes through the point \(P ( - 1,3 )\) and is such that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 1 } { x ^ { 2 } } , \quad x \neq 0 .$$
- Using integration, find \(\mathrm { f } ( x )\).
- Sketch the curve \(y = \mathrm { f } ( x )\) and write down the equations of its asymptotes.