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The diagram shows a curve \(C\) for which \(y\) is inversely proportional to \(x\). The curve passes through the point \(\left( 1 , - \frac { 1 } { 2 } \right)\).
- Determine the equation of the gradient function for the curve \(C\).
- Sketch this gradient function on the axes in the Printed Answer Booklet.
- The diagram indicates that the curve \(C\) has no stationary points.
State what feature of your sketch in part (a)(ii) corresponds to this.
- The curve \(C\) is translated by the vector \(\binom { - 2 } { 0 }\).
Find the equation of the curve after it has been translated.