Dmytro F.

asked • 12/12/20

How to solve such?

Hi. My daughter got this and we don't understand how to solve it.


'Find the conditions for a and b that make {(a, b), (-a, b), (2a, b), (a², b)} a function.'


I don't want the solution for exactly this, just want to understand how to solve such problems in general.

P.s.: 10th grade, need to solve it without usage of derivative. Thanks!

Gerard M.

It seems that that set of points always defines a function because a particular "a" value can never have two different outputs, since all the outputs are the same value, "b". Is there any additional context for this problem? Are there similar problems in the textbook or assigned? Are you sure all the y-coordinates are just "b"? I'll try to provide an answer if so :)
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12/13/20

Dmytro F.

No additional context, that's all we got
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12/13/20

Dmytro F.

Yes, all y-coordinates are just 'b'
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12/13/20

Dmytro F.

I ofc can see that a function that for sure satisfies all the conditions of the problem is 'y=b' but how to come to it logically, needed the solution itself.
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12/14/20

1 Expert Answer

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Mike D. answered • 12/13/20

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It's a function if for a given x, there is at most one y value.

So (1,2) (2,3) (3,4) would define a function but (1,2) (1,3) (2,3) (3,4) not because when x=1 there are two y values 2 and 3

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Dmytro F.

Thanks for your reply! But still, there is at most one 'y' value for any given 'x' in the condition. And it asks to 'Find the conditions.'
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12/14/20

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