What is meaning concretely than an expression is $Z_2$ symmetric under a certain transformation ?
Does is mean that the expression is the same when we do the transformation ? Does is mean that the expression is the opposite when we do the transformation ?
For the context : I have in mind the expression of a Beyond Standard Model Higgs potential :
It is said in an article than a $Z_2$ discrete symmetry is applied the potential (a function of $\phi_1$ and $\phi_2$) : "a $Z_2$ discrete symmetry of the form $\phi_1\rightarrow -\phi_1$ is imposed on the potential".
https://www.itp.kit.edu/_media/publications/masterthesismarcel.pdf page 8