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# 3: Functions

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• 3.1: Introduction to Functions
Our development of the function concept is a modern one, but quite quick, particularly in light of the fact that today’s definition took over 300 years to reach its present state. We begin with the definition of a relation.
• 3.2: Relations and Functions
• 3.3: Interpreting the Graph of a Function
In the previous section, we began with a function and then drew the graph of the given function. In this section, we will start with the graph of a function, then make a number of interpretations based on the given graph: function evaluations, the domain and range of the function, and solving equations and inequalities.
• 3.4: The Toolbox Functions
• 3.5: Absolute Value Functions
There are a few ways to describe what is meant by the absolute value |x| of a real number x. The long and short of both of these procedures is that |x| takes negative real numbers and assigns them to their positive counterparts while it leaves positive numbers alone. This last description is the one we shall adopt, and is summarized and discuss in this Module.