The Collatz conjecture is an open problem involving the 3x + 1 function. The function belongs to a class of generalized 3x + 1 functions of relatively prime type. This paper focuses on exploring periodic cycles for an extension of a generalized 3x + 1 function of relatively prime type. By extending its domain to \mathbb{R}, the result shows that every integer periodic point is isolated in the usual topology on \mathbb{R}. Moreover, every positive integer periodic cycle for the extension is attracting if the generalized 3x + 1 function is satisfied by parameters under some conditions.



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 Sriwongsa, Songpon, Ngiamsunthorn, Parinya Sa, Sindee, Sutthipong