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Chapter 5

# Formulating Functions

In This Chapter

Determining how much functions are worth

Checking the restrictions on input and output: Domain and range

Defining functions by their characteristics

Performing operations on functions

Looking at and creating inverse functions

A function is a very special type of relationship in mathematics. Functions are those relationships between input values and output values that guarantee that you’ll never get more than one output for any input. For example, the equation y = 8x + 2x2 – 3x is a function, because when you plug in any value for x, such as 2, you get only one value for y; in this case, y = 15. This characteristic of having just one value when you put a number into a function is essential when you’re dealing with functions that model the cost of production or the number of amoebas in a culture. You don’t want to be saying, “Well, there are either 16 or 16,000,000 amoebas in that dish.” You’d prefer just one answer when you use the formula. ...

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