The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit assumptions when modeling data with functions, and this article addresses two points that are commonly overlooked: 1. An "n"th-degree polynomial is not the only type of function that can model data with constant "n"th differences over equal-size intervals. 2. An "n"th-degree polynomial is, however, the only type of function with domain R that has constant "n"th differences over equal-size intervals without restricting interval size or input values.