This paper documents how eight high school students in a precalculus class enhanced with graphing calculators think about functions. Three models of thinking about functions emerged from students' function images observed over a period of 9 months. In the graph model, students believed that functions are essentially graphs; in the equation model, they believed that functions are relationships between x and y expressed by equations; and in the unique correspondence model, they took "one output for every input" as the definition of a function. The vertical line test served as a link across all of the models. (SW)