Sketch the curve with equation
$$y = k - \frac { 1 } { 2 x } \quad \text { where } k \text { is a positive constant }$$
State, in terms of \(k\), the coordinates of any points of intersection with the coordinate axes and the equation of the horizontal asymptote.
The straight line \(l\) has equation \(y = 2 x + 3\)
Given that \(l\) cuts the curve in two distinct places,
find the range of values of \(k\), writing your answer in set notation.