LN8(FUNCTION)(1) - FUNCTION As a Rule As a Set of Ordered...

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FUNCTION As a Rule As a Set of Ordered Pairs
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Concept of function We may imagine a function to be some sort of a box or machine. When something is fed into the machine, there will be an output. The output must be unique. This means that no matter how many times a particular input is used, the same output is obtained. (input) (output)
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Function as a rule Consider a function that gives outputs shown in the table below. Input, 0 2 3 4 6 Output, 0 4 9 9 16 36 Examination of the table seems to indicate that if then . The rule is: “Square the input” and the answer is the output. The function may be written as (a) or (b) .
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If a function is given in equation form, we define the domain of the function to be the set of all allowable values of while the range is the set of all arising values of . Some examples are given below. Function Domain Range All real numbers All real numbers except 1 and
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Graph of a function Let be a function with domain . The graph of is the set of all points where and . Since there is only one value of the function for a given it follows that no vertical line can contain two points in the graph of a function. This is known as the vertical line test for a function. An equivalent statement is as follows: A graph represents a function if no vertical line cuts the graph at two or more points.
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