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Mapping and functions

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?

Reply 1

B_9710

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.

Reply 2

Notnek

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.

(edited 7 years ago)

Reply 3

B_9710

Original post by Rana1997

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