Question

identify whether the graph of the function f(x) shown below is even, odd, or neither.
it is symmetrical about the origin
it is symmetrical about the y-axis
it is symmetrical about the x-axis
it is not symmetrical over the y-axis or about the origin

Explanation:

Step1: Recall Symmetry Rules

For a function to be even, its graph is symmetric about the \( y \)-axis (i.e., \( f(-x)=f(x) \)). For a function to be odd, its graph is symmetric about the origin (i.e., \( f(-x)= -f(x) \)). A function is neither if it lacks both symmetries.

Step2: Analyze the Graph

Visually inspect the graph. The left - hand side (for negative \( x \)) and the right - hand side (for positive \( x \)) do not mirror over the \( y \)-axis (so not even). Also, reflecting over the origin (rotating 180° about the origin) does not map the graph onto itself (so not odd). So the graph is not symmetric about the \( y \)-axis or the origin.

Answer:

The function's graph is neither even nor odd (it is not symmetrical over the \( y \)-axis or about the origin).