Function

Things to remember

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• To be a relation a function all the elements of the domain must have 9image in co-domain. Otherwise, it will not be the function.
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• Also, the condition for uniqueness should be a function exist. Instead of these, the function can also be tested by using a test known as vertical line test. For this test, a vertical line is drawn in the graph at any point. If the vertical line cuts the graph at only one point it is a function and if it cuts at more than one point then it is not a function.
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  Main features of a function

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  1. to every x∈A,there exists an element y∈B such that (x,y)∈f i.e. y is an image of x under f i.e. y = f(x).
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  2. no element of A can have more than one image in B.
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  3. there may be elements of B which are not associated with any element of A.
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  4. distinct elements of A may have the same image in B.
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