Determine if the function $f$ is even, odd or neither given the graph of $f$ The following picture is a graph of a function $f$. I am to determine whether the function is even, odd, or neither. I reasoned that $f$ is odd, because if the graph is rotated $\pi$ radians, the graph is reproduced perfectly. The graph is clearly not even, because it is not symmetrical with respect to the vertical axis. However, the solution states that $f$ is neither even or odd, and I do not understand why.



"I reasoned that $f$ is odd, because if the graph is rotated $\pi$ radians, the graph is reproduced perfectly."

It sounds like you were rotating around  the $y$-intercept.  To test for oddness, you always want to rotate around the origin.  A quick test for non-oddness is to look at the origin.  If the graph doesn't go through the origin, the function is not odd.  If the graph does go through the origin then the function may or may not be odd.  It is in this case that you'll need to check the rotation of $\pi$ radians.
