Determine whether the function is even, odd, or neither.

Question

Quizplus · Accepted Answer

The given function is not an algebraic expression or equation, so we cannot determine whether it is even, odd, or neither without more information. It is not possible to determine the evenness or oddness of a function just from its expression or name. We need to know the explicit formula or a graph of the function. However, even and odd functions have some specific properties which we can use to identify them. An even function satisfies $f(-x)=f(x)$ for all $x$ in its domain, which means that its graph is symmetric with respect to the $y$-axis. An odd function satisfies $f(-x)=-f(x)$ for all $x$ in its domain, which means that its graph is symmetric with respect to the origin. If neither of these properties hold, then the function is neither even nor odd.

Determine Whether the Function Is Even, Odd, or Neither