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EXAMPLES OF FUNCTIONS
What is a Function?
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
Example 1: Is the relation expressed in the mapping diagram a function?
Each element of the domain is being traced to one and only element in the range. However, it is okay for two or more values in the domain to share a common value in the range. That is, even though the elements 5 and 10 in the domain share the same value of 2 in the range, this relation is still a function.
Example 2: Is the relation expressed in the mapping diagram a function?
What do you think? Does each value in the domain point to a single value in the range? Absolutely! There’s nothing wrong when four elements coming from the domain are sharing a common value in the range. This is a great example of a function as well.
Example 3: Is the relation expressed in the mapping diagram a function?
Messy? Yes! Confusing? Not really. The only thing I am after is to observe if an element in the domain is being “greedy” by wanting to be paired with more than one element in the range. The element 15 has two arrows pointing to 7 and 9. This is a clear violation of the requirement to be a function. A function is well behaved, that is, each element in the domain must point to one element in the range. Therefore, this relation is not a function.
Example 4: Is the relation expressed in the mapping diagram a function?
If you think example #3 was bad, this example is the absolute worst! A single element in the domain is paired with four elements in the range. Remember, if an element in the domain is associated with more than one element in the range, the relation is automatically disqualified as a function. Thus, this relation is absolutely not a function.
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