Sketch the graph of \(y = \frac { 1 } { x }\), where \(x \neq 0\), showing the parts of the graph corresponding to both positive and negative values of \(x\).
Describe fully the geometrical transformation that transforms the curve \(y = \frac { 1 } { x }\) to the curve \(y = \frac { 1 } { x + 2 }\). Hence sketch the curve \(y = \frac { 1 } { x + 2 }\).
Differentiate \(\frac { 1 } { x }\) with respect to \(x\).
Use parts (ii) and (iii) to find the gradient of the curve \(y = \frac { 1 } { x + 2 }\) at the point where it crosses the \(y\)-axis.