Question

Pls help with practice!According to the graph, is f even, odd or neither?

Answer 1

Consider the following conditions for a function,

`\begin{gathered} f(-x)=f(x)\Leftrightarrow\text{ Even Function} \\ f(-x)=-f(x)\Leftrightarrow\text{ Odd Function} \end{gathered}`

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.