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

Explanation:

Step1: Recall function - type definitions

An even function satisfies $f(x)=f( - x)$ (symmetric about y - axis), and an odd function satisfies $f(-x)=-f(x)$ (symmetric about the origin).

Step2: Check for y - axis symmetry

For a function to be even, for every point $(x,y)$ on the graph, the point $(-x,y)$ must also be on the graph. Looking at the given graph, if we take a point on the right - hand side of the y - axis, say $(x,y)$ where $x>0$, the corresponding point $(-x,y)$ is not on the graph. So it is not an even function.

Step3: Check for origin symmetry

For a function to be odd, for every point $(x,y)$ on the graph, the point $(-x,-y)$ must be on the graph. Looking at the given graph, if we take a point on the right - hand side of the y - axis, say $(x,y)$ where $x > 0$, the corresponding point $(-x,-y)$ is not on the graph. So it is not an odd function.

Answer:

Neither