Functions

Abstract

You have encountered functions repeatedly in your previous mathematics courses. In high school you learned about polynomial, exponential, logarithmic and trigonometric functions, among others. Though logarithms and trigonometry are often first learned about without thinking about functions (for example, sines and cosines can be thought of in terms of solving right triangles), in many pre-calculus courses, and certainly in calculus, the focus shifts to functions (for example, thinking of sine and cosine as functions defined on the entire real number line). In calculus, the operation of taking a derivative is something that takes functions, and gives us new functions (namely the derivatives of the original ones). In applications of calculus, such as in physics or chemistry, thinking of exponentials, sines, cosines, etc. as functions is crucial. For example, we use sine and cosine functions to describe simple harmonic motion.

A function is the abstract image of the dependence of one magnitude on another.

A. D. Aleksandrov (1912–1999)