Symmetry in Graphs: Conditions & Possibilities

[Danish_Khatri]

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?

 

[tiny-tim]

Welcome to PF!

Hi Danish_Khatri! Welcome to PF!

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 …

 

[Danish_Khatri]

Thanks for your help dear... :-)