60 2 A Look Back So far, our discussion has focused on solving equations and developing techniques for graphing equations containing two variables. A Look Ahead In this chapter, we look at a special type of equation involving two variables called a function . This chapter deals with what a function is, how to graph functions, properties of functions, and how functions are used in applications. The word function apparently was introduced by René Descartes in 1637. For him, a function was simply any positive integer power of a variable x. Gottfried Wilhelm Leibniz (1646—1716), who always emphasized the geometric side of mathematics, used the word function to denote any quantity associated with a curve, such as the coordinates of a point on the curve. Leonhard Euler (1707—1783) used the word to mean any equation or formula involving variables and constants. His idea of a function is similar to the one most often seen in courses that precede calculus. Later, the use of functions in investigating heat flow equations led to a very broad definition that originated with Lejeune Dirichlet (1805—1859), which describes a function as a correspondence between two sets. That is the definition used in this text. Choosing a Data Plan When selecting a data plan for a device, most consumers choose a service provider first and then select an appropriate data plan from that provider. The choice as to the type of plan selected depends on your use of the device. For example, is online gaming important? Do you want to stream audio or video? The mathematics learned in this chapter can help you decide what plan is best suited to your particular needs. —See the Internet-based Chapter Project— Outline 2. 1 Functions 2. 2 The Graph of a Function 2. 3 Properties of Functions 2. 4 Library of Functions; Piecewise-defined Functions 2. 5 Graphing Techniques: Transformations 2. 6 Mathematical Models: Building Functions Chapter Review Chapter Test Cumulative Review Chapter Project Functions and Their Graphs Credit: Oleksiy Mark/Shutterstock
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