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    Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?

    Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
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    All elements from set A have to be mapped to set B to be a function. What's more, an element in A can only be mapped to one element in B but every element in B need not be mapped to from A.
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    (Original post by Rana1997)
    Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?
    Every element of the domain must be mapped for it to be a function.

    So the answer to your question is no.

    Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
    Functions can be continuous and discontinuous. 3 is mapped so that is a function with domain x>0.
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    (Original post by Rana1997)
    Consider a rule that maps set A to set B in a one-to-one mapping. However it does not map every element of A. Is it a function?

    Also if a mapping has several rules for several conditions and it happens that the graph is not continuous (such as f(x)=x^2 for 0< x < 3, f(x)= 10x for x>=3) is it a function?
    All because the graph is discontinuous doesn't mean the mapping cannot be a function. You can have functions that are discrete. There's is a notion that functions can be either continuous or discontinuous.
    The function  y=\sin x /x, x\neq 0 is a function though not continuous.
 
 
 
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