In this chapter, we will discuss several principles of graphing that we will rely on throughout the rest of the text. In the past, you have probably either relied on the most basic practice of "plotting points" or on technology, such as graphing calculators, to create graphs. We will begin by looking at the limitations of both of these approaches. We will begin to investigate how the algebraic process of composition with basic arithmetic functions affects a function both numerically and graphically. We will then see how these principles can be used to view linear function in a new, dynamic way. We will then continue to develop a method of graphing a function that is built-up by arithmetic operations from a known "core" function. We will conclude the chapter by showing how to try and uncover the formula for a function from either its numerical or graphical description. Along the way, we will learn to use the Java-based graphing tool, XFunctions.
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