What is a function? A function from X to Y is a relation between X and Y that has the property that any two ordered pairs with the same x-value also have the same y-value. It is a correspondance that assigns to each number x in X exactly one number y in Y. Basically, X and Y are sets and there exists one number (x) in the set X that corresponds with one number (y) in the set Y.

When dealing with functions, there are two basic types: the on-to function and the one-to-one function. A function is on-to if it it's range consists of all the values in the the set Y and it is one-to-one if there is one and only one x-value for each y-value in each of the sets. Below are some example of functions, see if you can determine whether they are on-to or one-to-one.

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