Chapter 5

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* = 8*x* + 2*x*^{2} – 3^{x} 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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