Precalculus: Functions

Functions

Calculus is the mathematical study of change, and real-life things that change are modeled by functions. Precalculus is essentially the study of functions, with a few other related topics that supplement the study of functions and prepare students for calculus. In this text we'll concern ourselves first with learning about general functions, and later with certain types of common functions with special properties, like polynomial, exponential, logarithmic, and trigonometric functions. First, it is of critical importance to understand exactly what a function is. In the following lessons, we'll discuss what makes a function a function, some general properties of functions, and a few basic categories of functions. In this text we'll assume a general knowledge of algebraic principles of solving equations, working with the real numbers, and working with sets. In the last of the upcoming sections, we'll learn how functions behave under operations like addition, subtraction, etc.