Answer
See explanation
Work Step by Step
The level surfaces for \(f(x,y,z)\) result in \[ f(x,y,z) = k, \quad k \in \mathbb{R} \] Since \(f(x,y,z) = x^2 + z^2\), the level surface is given by \[ x^2 + z^2 = k \] We can note that \(x^2 + z^2 \geq 0\) for any real values \(x, y, z\), then \(k \geq 0\). Since \(k \geq 0\) and \(x^2 + z^2 = k\) do not depend on \(y\), the surface represents cylinders with a symmetric axis along the \(y\)-axis.
