Question

find the graph of an odd function.

Explanation:

Define odd function symmetry

An odd function satisfies \(f(-x) = -f(x)\).
Its graph is symmetric about the origin.
Rotating it \(180^\circ\) leaves it unchanged.

Analyze top-left graph

The graph is symmetric about the y-axis.
This represents an even function, not odd.

Analyze top-right graph

The graph is symmetric about the y-axis.
This represents an even function, not odd.

Analyze bottom-left graph

The graph is symmetric about the origin.
Rotating it \(180^\circ\) yields the same graph.
This represents an odd function.

Analyze bottom-right graph

The graph has no origin symmetry.
It is neither even nor odd.

Answer:

• (A) Top-left graph (symmetric about the y-axis)
• (B) Top-right graph (symmetric about the y-axis)
• (C) Bottom-left graph (symmetric about the origin) (Correct answer)
• (D) Bottom-right graph (no origin symmetry)