Modeling Concepts, Visualization, and Interpretation

Mathematical modeling is a broad subject. Essentially, when a non-mathematical scenario is described using an equation or equations or by a set of mathematical rules, those equations or rules are called mathematical models. Creating a mathematical model involves understanding how to quantify events or changes, and using a model requires understanding both the mathematics and how the representation is defined. Many mathematical models are based on concepts from calculus. The intricate models are often evaluated based on graphical results, and interpretations can be made based on visual output. The chapter focuses on a review of calculus concepts related to graphical shape of functions and how to describe these aspects. Functions are often described explicitly, meaning that the output is calculated using a specific algebraic definition. The chapter provides some ways of transforming functions and how to connect changes in function definition to graphical changes.