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Topic: Re: AP-CALC digest 393
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Posts: 12
Registered: 12/6/04
Re: AP-CALC digest 393
Posted: Sep 18, 1998 12:04 AM
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In a message dated 98-09-17 16:03:39 EDT, Mary Harrison wrote:

<< Topic of conversation in the math office today:
Is it possible for a function or relation to be both symmetric to the y
axis and to the origin but not to the x-axis?

The only thing I could think of was 3/4 of a circle.

Anything else? Other than variations of this (e.g. triangle segments)
3/4 circle is not symmetric to the origin!! The answer to the question is
"NO." If the relation R is symmetric wrt y axis and origin, and (x, y) is an
element of R, then (-x, y) is an element of R as is (-x, -y). Then, since
(-x, y) is an element of R, (x, -y) -- the reflection of (-x, y) wrt the
origin -- is also an element of R. So (x, y) element of R implies (x, -y) is
an element of R, and R is also symmetric wrt x axis!!

Martha Gregg
Waverly, NE

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