Consider the following conditions for a function,
[tex]\begin{gathered} f(-x)=f(x)\Leftrightarrow\text{ Even Function} \\ f(-x)=-f(x)\Leftrightarrow\text{ Odd Function} \end{gathered}[/tex]
It follows that the curve of an even function will be symmetric about the y-axis, while the curve of an odd function will be symmetric about the origin.
Now, observe the given graph carefully.
It is evident that the function is not symmetric about the y-axis. Also, it is not symmetric about the origin as well.
Therefore, it can be concluded that the function is neither even nor odd.
