y=f(x) is even when f(- x)=f(x) for each x in the domain of f. The graph of an even function is symmetric about the y-axis.
y=f(x) is odd when f(- x)=- f(x) for each x in the domain of f. The graph of an odd function is symmetric about the origin — it looks the same after a rotation of 180^(∘).
With these definitions in mind, let's consider the given graph.
We see that the graph is not symmetric about the y-axis, so it does not belong to an even function. We also see that the graph is not symmetric about the origin, so it does not belong to an odd function. Therefore, the function represented by the graph is neither even nor odd.
