many to one or one to many maths problem

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pondering-soul
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Could someone please clarify if the mark scheme is wrong and it is many to one AND one to many... or just one to many?Image

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thanks for any help I appreciate it
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Smallwatch
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The mark scheme is correct, an ellipse can never be many-to-one.

Many-to-one means that two x values are put in the function, and both will give the same result.
e.g

f(x)=x^{2}+3x+2

If you did f(-2) and f(-1) they would both give 0, the same y value, and only this value.

Your example does not work in the same way, because each x value corresponds to two y values, which means it must be one-to-many.
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ghostwalker
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Interestingly, the "Cambridge International AS and A level mathematics" (2012 ISBN 978 1444 14644 8) describes a circle, which is very similar object to the one in this question, as many-many. And that is how I would describe it.

However, looking at at least one of the current syllabii - and this question - they only mention, one-one, one-many, and many-one. What's happened to "many-many"?

Is there something in how they've been defined that says if it's one-many then it can't be many-one as well. :iiam:

Any teachers/educators in the know?
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pondering-soul
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(Original post by ghostwalker)
Interestingly, the "Cambridge International AS and A level mathematics" (2012 ISBN 978 1444 14644 8) describes a circle, which is very similar object to the one in this question, as many-many. And that is how I would describe it.

However, looking at at least one of the current syllabii - and this question - they only mention, one-one, one-many, and many-one. What's happened to "many-many"?

Is there something in how they've been defined that says if it's one-many then it can't be many-one as well. :iiam:

Any teachers/educators in the know?
That was my initial thought aswell... perhaps it's because the definition of many-to-one might be where two or more x values correspond to only one y value. However, from the circle or elipses... we can't ever get a scenario where 2 x values = ONLY 1 y value because for every point of x within the range of the equation, there are always 2 y values... so its not 2 x = 1 y value, its more like, 2 x value = 2 y value... ?
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pondering-soul
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(Original post by Smallwatch)
The mark scheme is correct, an ellipse can never be many-to-one.

Many-to-one means that two x values are put in the function, and both will give the same result.
e.g

f(x)=x^{2}+3x+2

If you did f(-2) and f(-1) they would both give 0, the same y value, and only this value.

Your example does not work in the same way, because each x value corresponds to two y values, which means it must be one-to-many.
So for a function to be many to one it must be 2 x = 1 y value, but since EVERY x value is always equal to 2 y values, there is never a scenario for 2 x = 1 y value and so it can never be many to one?
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ghostwalker
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(Original post by pondering-soul)
That was my initial thought aswell... perhaps it's because the definition of many-to-one might be where two or more x values correspond to only one y value. However, from the circle or elipses... we can't ever get a scenario where 2 x values = ONLY 1 y value because for every point of x within the range of the equation, there are always 2 y values... so its not 2 x = 1 y value, its more like, 2 x value = 2 y value... ?
For it to be many-one, we only require one y-value to have more than one corresponding x-value. In a Similar fashion for one-many.

The extremes of the ellipse along the x-axis are an example of where we have two x-values and only 1 y-value.
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pondering-soul
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(Original post by ghostwalker)
For it to be many-one, we only require one y-value to have more than one corresponding x-value. In a Similar fashion for one-many.

The extremes of the ellipse along the x-axis are an example of where we have two x-values and only 1 y-value.
oh wow I never thought of that... perhaps it's just a matter of my textbook only having those 3 limited definitions and no 'many-to-many' definition. I'll just ask my teacher if it's a problem with the specific curriculum, thanks for the help man
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