Symmetry in Graphs: Conditions & Possibilities

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SUMMARY

This discussion centers on the conditions for symmetry in graphs of functions. A graph is symmetric about the y-axis if for every point (x,y), the point (-x,y) also exists. It is symmetric about the x-axis if for every point (x,y), the point (x,-y) exists, and symmetric about the origin if for every point (x,y), the point (-x,-y) exists. The conversation raises the question of whether a graph can satisfy one of these conditions without appearing symmetric, highlighting the complexity of visual representation versus mathematical definition.

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Danish_Khatri
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For a graph of any function, one of following conditions is said to exist so as for it to be symmetric:
a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists.
a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists.
a graph is symmetric about origin if along with a point (x,y) a point (-x, -y) exists.
isn't it possible that one of the above condition is satisfied but still the graph is not symmetric. what i want to say is that can't it be possible for a curve to have such shape that it does not look symmetric but still passes through the two points highlighted by one of the conditions mentioned above?
 
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Welcome to PF!

Hi Danish_Khatri! Welcome to PF! :wink:
Danish_Khatri said:
For a graph of any function, one of following conditions is said to exist so as for it to be symmetric:
a graph is symmetric about y-axis if along with a point (x,y) a point (-x, y) exists.
a graph is symmetric about x-axis if along with a point (x,y) a point (x, -y) exists.
a graph is symmetric about origin if along with a point (x,y) a point (-x, -y) exists.
isn't it possible that one of the above condition is satisfied but still the graph is not symmetric. what i want to say is that can't it be possible for a curve to have such shape that it does not look symmetric but still passes through the two points highlighted by one of the conditions mentioned above?

I think it means for every (x,y) on the curve … :smile:
 
Thanks for your help dear... :-)
 

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