ROC of transfer function
For that transfer function, you have 2 regions of convergence (ROCs): $R_1 = \{|z|&gt;0.5\}$ and $R_2=\{|z|&lt;0.5\}$.

$R_1$ includes the unit circle, so the corresponding impulse response corresponds to a BIBO-stable filter. Since it is an outer disc, it is also right-sided.

Conversely, $R_2$ corresponds to a left-sided impulse response, and an unstable filter.

The extra $z$ in the numerator means that the impulse responses will be shifted 1 sample to the left, so the impulse responses are not causal.