Question

identify whether the graph of the function f(x) shown below is even, odd, or neither.

Explanation:

Step1: Recall the definitions of even and odd functions

An even function satisfies \( f(x)=f(-x) \) for all \( x \) in its domain, and its graph is symmetric about the \( y \)-axis. An odd function satisfies \( f(-x)=-f(x) \) for all \( x \) in its domain, and its graph is symmetric about the origin.

Step2: Check the symmetry of the given graph

Looking at the graph, there is no symmetry about the \( y \)-axis (since for example, if we consider a non - zero \( x \) value where the function is defined, there is no corresponding point at \( -x \) with the same \( y \) - value). Also, there is no symmetry about the origin (since for a non - zero \( x \) value where the function is defined, there is no corresponding point at \( -x \) with the negative \( y \) - value).

Answer:

Neither