Relations and Functions

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In this section, we answer the question: What is a Function in Math. The basic idea of a function first starts with an understanding of a relation. A relation is nothing more than any set of ordered pairs. A function is a special type of relation, where each x-value corresponds to or is linked up with exactly one y-value. It is often said that for each "x", there can be only one "y". When we have a function, it is crystal clear what the value is for y, given a certain x-value. As an example of something that is not a function:{(6,2),(3,7),(6,-4)}. We can see in this example, the x-value of 6 corresponds to two different y-values: 2 and -4. This is a violation of the definition of a function. If we had a function, the x-value of 6 should only correspond to exactly one y-value. As an example of a function:{(3,5),(-2,7),(4,12)}. In this case, each x-value corresponds to only one y-value. The x-value of 3 corresponds to a y-value of 5. The x-value of -2 corresponds to a y-value of 7. Lastly, the x-value of 4 corresponds to a y-value of 12.
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