Symmetry

  Plot[Cos[x],{x,-2 Pi,2 Pi},AspectRatio->Automatic];

In[4]:=

  Plot[Sin[x],{x,-2 Pi,2 Pi},AspectRatio->Automatic];

The graph of an even function is symmetric with respect to the y axis.
The graph of an odd function is symmetric with respect to the origin.

Look at the graphs of x^k.

In[5]:=

  p=Table[Plot[x^k,{x,-2,2},DisplayFunction->Identity],{k,1,6}];

In[6]:=

  Show[GraphicsArray[{Table[p[[k]],{k,1,2}],
   Table[p[[k]],{k,3,4}],Table[p[[k]],{k,5,6}]}]];

Out[6]

Notice anything?

Notice anything? ...

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