Question

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

the graph is neither because it is symmetrical about the y - axis

Explanation:

Step1: Recall symmetry rules

For a function to be even, its graph is symmetric about the \( y \)-axis (\( f(-x)=f(x) \)). For odd, symmetric about the origin (\( f(-x)=-f(x) \)).

Step2: Analyze the graph

Visually, the left and right sides of the graph don't mirror over the \( y \)-axis (e.g., check points: left side has a peak at \( x=-1 \), right side doesn't mirror that at \( x = 1 \)) and also doesn't mirror over the origin (since symmetry about origin would require \( (x,y) \) and \( (-x,-y) \) to be on the graph, which isn't the case here). So it's neither. The previous reason was incorrect; the graph isn't symmetric about \( y \)-axis. Correctly, it lacks both \( y \)-axis and origin symmetry.

Answer:

The graph is neither because it does not exhibit symmetry about the \( y \)-axis (even function) or about the origin (odd function).