What is a Function, Anyway? Domain? Range?

Next time you're at a fast-food restaurant, take a look at the price list. It may look something like this:
• Hamburger..................$1.50
• Cheeseburger..............$2.00
• French Fries................$1.00
• Soda.........................$1.00

This is an example of a function: the "price" function. For every food item on the menu, there is a price. In the English language, we can say:
The price of French fries is $1.00

The domain of this function is the set {Hamburger, Cheeseburger, French Fries, Soda}. The range of the function is the set {$1.00, $1.50,$ 2.00}.

For each item in the domain (like "Hamburger"), there is only one price. It wouldn't make sense to have two different prices listed for "Hamburger"! But notice that two different items may have the same price.
Now let's turn to a mathematical example. One simple example is the square function. Remember, to square a number is to multiply it by itself. You can say:

The square of 3 is 9.

We can even make a table, similar to the fast-food menu!