identify whether the graph of the function f(x) shown below is even, odd, or neither.\nanswer attempt 1 out…

Explanation:

Step1: Recall function - symmetry rules

An even - function has the property (f(x)=f( - x)) and its graph is symmetric about the (y) - axis. An odd - function has the property (f(-x)=-f(x)) and its graph is symmetric about the origin.

Step2: Check for (y) - axis symmetry

If we reflect the graph of (y = f(x)) across the (y) - axis, the resulting graph does not match the original graph. So, the function is not even.

Step3: Check for origin symmetry

If we rotate the graph of (y = f(x)) (180^{\circ}) about the origin, the resulting graph matches the original graph. For any point ((x,y)) on the graph, the point ((-x,-y)) is also on the graph. This satisfies the property (f(-x)=-f(x)) of an odd function.

Answer:

odd; it is symmetric about the origin.