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This study empirically investigates how Generative AI (Gen AI) influences undergraduate writing by analyzing linguistic characteristics of analytical essays from first-year composition courses. Using Systemic Functional Linguistics (SFL) and corpus linguistics frameworks, essays were analyzed through Coh-Metrix, a computational tool for data mining textual complexity and coherence. The study compares student writing across three instructional contexts: classes explicitly allowing Gen-AI use, classes prohibiting it, and classes conducted before Gen-AI availability. Results reveal that AI-permitted contexts produced essays with greater lexical sophistication but lower referential cohesion and altered syntactic structures. These findings highlight critical implications for educators: integrating AI tools can enhance vocabulary and style but may disrupt traditional academic coherence, guiding balanced AI integration to strengthen foundational writing skills.