Subjects algebra

Odd Function C24A77

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1. **Problem Statement:** Identify the graph of an odd function among the given four graphs. 2. **Definition of Odd Function:** A function $f(x)$ is odd if it satisfies the condition: $$f(-x) = -f(x)$$ This means the graph is symmetric with respect to the origin. 3. **Analyzing the Graphs:** - Top-left and bottom-right graphs are parabolas opening upwards with vertex at $(0,1)$, which are not symmetric about the origin, so they are not odd. - Bottom-left graph resembles a cosine wave, which is an even function since $\cos(-x) = \cos(x)$. - Top-right graph resembles a sine wave, which is an odd function since $\sin(-x) = -\sin(x)$. 4. **Conclusion:** The top-right graph is the graph of the odd function because it passes through the origin and is symmetric with respect to the origin. **Final answer:** The graph of the odd function is the top-right sinusoidal graph.