8 A surface, \(C\), is given by the equation \(z = \mathrm { f } ( x , y )\) for all real values of \(x\) and \(y\). You are given that \(C\) has the following properties.
- The surface is continuous for all \(x\) and \(y\).
- The contour \(z = - 1\) is a single point on the \(z\)-axis.
- For \(- 1 < a < 1\), the contour \(z = a\) is a pair of circles with different radiuses but each having the same centre \(( 0,0 , a )\).
- The contour \(z = 1\) consists of the circle, centre \(( 0,0,1 )\) and radius 1 .
Sketch a possible section of \(C\) corresponding to \(y = 0\).