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Chapter 3

# Functioning Well

In This Chapter

Understanding why functions are your friends

Applying the inverse to a function

Moving a function around on a graph

You can't get very far in any mathematical discussion without encountering rules, patterns, operations, or relationships among the concepts you're discussing. One common theme in math is the relationship between certain values (often called the input and the output), which are the values you start with and the values you end up with, respectively. Functions are very special types of relationships using input and output values, and they play a big part in trigonometry. So, what distinguishes a relation from a function, and why should you care? The distinction is important in all mathematics, not just in trigonometry.

## Relations versus Functions

A relation in mathematics is a rule that creates a certain output for any given input. The input is the number you enter in place of a variable, and the output is the result(s) you get when you perform the operations for that relation. Each relation has a rule, or expression, that usually involves mathematical operations such as addition, subtraction, square roots, and so on. For instance, ...

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