graphics – Bloch ball for a given transformation

Given the transformation $r_x rightarrow r_xsqrt{1-g}, r_y rightarrow r_y sqrt{1-g}, r_z rightarrow g + r_z (1-g)$, how can one show this with a Bloch sphere/ball ?

Edit: What I meant by “show” is to take a unit sphere and then apply this transformation and see how it changes its shape/position (given that it may shrink and at the same time its center can be displaced).