9 The function f is defined by
$$f ( x ) = \frac { x ^ { 2 } + 2 x + 2 } { x ^ { 2 } }$$
- Write down the equations of the two asymptotes to the curve \(y = \mathrm { f } ( x )\).
- By considering the expression \(x ^ { 2 } + 2 x + 2\) :
- show that the graph of \(y = \mathrm { f } ( x )\) does not intersect the \(x\)-axis;
- find the non-real roots of the equation \(\mathrm { f } ( x ) = 0\).
- Show that, if the equation \(\mathrm { f } ( x ) = k\) has two equal roots, then
$$4 - 8 ( 1 - k ) = 0$$
- Deduce that the graph of \(y = \mathrm { f } ( x )\) has exactly one stationary point and find its coordinates.