PP Section 3.1

# PP Section 3.1 - The Definition of a Function Let X and Y...

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The Definition of a Function

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Let X and Y be two nonempty sets of real numbers. A function from X into Y is a relation that associates with each element of X a unique element of Y . The set X is called the domain of the function. For each element x in X , the corresponding element y in Y is called the image of x . The set of all images of the elements of the domain is called the range of the function.
DOMAIN RANGE X Y f x x x y y

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Example: Which of the following relations are function? {(1, 1), (2, 4), (3, 9), (-3, 9)} {(1, 1), (1, -1), (2, 4), (4, 9)} A Function Not A Function
Functions are often denoted by letters such as f, F, g, G, and others. The symbol f(x) , read “ f of x ” or “ f at x ”, is the number that results when x is given and the function f is applied. Elements of the domain, x, can be though of as input and the result obtained when the function is applied can be though of as output. Restrictions on this input/output machine:

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PP Section 3.1 - The Definition of a Function Let X and Y...

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