Really i want to know if i can show the parity of any numerical function if i have only the table of it variation , for example if i take the below table of variation of the function $f$ defined over $[-2,2] $
> \begin{array}{c|cc|} x & -2 & 0 & 2\\ \hline f(x) & 4 \searrow & 0 & \nearrow 4 \end{array} Then is it possible to say the function $f$ is even since satisfy the symetric domain ?
No The table of variations contains only the intervals where the function is monotonic and the amplitude of the variations on these intervals. These details don't suffice to say if a function is even.