# Functions

Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

## Abstract

The reader has encountered functions repeatedly in previous mathematics courses. In high school one learns about polynomial, exponential, logarithmic and trigonometric functions, among others. Although logarithms and trigonometry are often first encountered without thinking about functions (for example, sines and cosines are thought of in terms of solving right triangles), in calculus courses and above the focus shifts to the point of view of functions (for example, thinking of sine and cosine as functions defined on the entire real number line). The operation of taking a derivative, for example, is something that is done to functions. In applications of calculus, such as in physics or chemistry, it is crucial to think of exponentials, sines and cosines as functions. For example, sine and cosine functions are used to describe simple harmonic motion.

## Keywords

Inverse Function Commutative Diagram Inverse Image Coordinate Function Bijective Function

## Authors and Affiliations

1. 1.Mathematics DepartmentBard CollegeAnnandale-on-HudsonUSA