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C3 Functions

Am I correct in saying that for C3 Functions, the below is the correct definition:

For each value of x in the domain there is only one value of y in the range.

Hence, the picture below means that it is not a many-to-one function as the values of x do not map onto a single value of y in the range (they map onto two values of y in the range) and therefore it is not a function.

Original post by Noah~
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You're right. Suppose XX and YY are two sets. A function maps each element of XX to a unique element of YY (i.e. it's a one-to-one association of the two sets).
(edited 10 years ago)
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davros
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Original post by Noah~
Am I correct in saying that for C3 Functions, the below is the correct definition:

For each value of x in the domain there is only one value of y in the range.

Hence, the picture below means that it is not a many-to-one function as the values of x do not map onto a single value of y in the range (they map onto two values of y in the range) and therefore it is not a function.



That looks correct if I've interpreted that diagram correctly - it's trying to map one value to two outputs so it's not a function.
Reply 3
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Noah~
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Original post by Khallil
You're right. Suppose XX and YY are two sets. A function maps each element of XX to a unique element of YY (i.e. it's a one-to-one association of the two sets).


Original post by davros
That looks correct if I've interpreted that diagram correctly - it's trying to map one value to two outputs so it's not a function.


Thanks.

For the graph below, would it also not be considered a function because the elements to the left of where the curve cuts the x-axis, those elements are not mapped to any elements of Y at all (the values are not mapped anywhere) hence it is also not a function.

Reply 4
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davros
16
Original post by Noah~
Thanks.

For the graph below, would it also not be considered a function because the elements to the left of where the curve cuts the x-axis, those elements are not mapped to any elements of Y at all (the values are not mapped anywhere) hence it is also not a function.



Well if you restrict your domain, that's not really a problem!

The real problem here is that to the right of the vertex each x value maps to 2 y values, so again this isn't a function (or at least, you can't write y = f(x) with f(x) being a function).
Original post by Noah~


The fact the elements of XX to the left of where the curve cuts the x-axis aren't mapped to elements of YY is irrelevant. A function doesn't need to be defined for all x∈Rx \in \mathbb{R}. It can be defined for as many or as little elements of XX that you choose, so long as they are uniquely matched up to elements of YY.

The main problem with that not being a function is that it maps one element of the domain to two elements in the range (apart from where the curve cuts the x-axis) and that's why it can't be considered a function.

I'm guessing this curve is of the form y2=x+ay^2 = x + a. It would be a function if you restricted the curve to the positive square root of x+ax+a.
(edited 10 years ago)

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