My question is that if you know a graph has asymtotes then it is not a function because the value of x does not map onto a value of y for the asymtote and we know that functions can either be one to one or many to one BUT THEN why do asymtotic graphs sometimes be one to one or many to one eventhough they are not functions??
Functions mappings
- Thread starter Vikash
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Help is really appreciated.
Dr.Peterson
Elite Member
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- Nov 12, 2017
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I assume you are referring to vertical asymptotets, and that you are claiming that if any value of x is not in the domain, then it is not a function. That is utterly untrue! All it means is that it is a function on a smaller domain than the set of real numbers.
The definition of a function is that it is a relation such that, for any value in the domain, there is only one corresponding value in the range. It says nothing about the domain having to be all real numbers.
When the "vertical line test" is stated, too often people say that every vertical line must pass through exactly one point on the graph, which leads to your apparent misconception. No, every vertical line must pass through no more than one point on the graph; it may pass through none.
