If \( f \) is an odd function, then \( f(-x)= \) The graph of an odd function is symmetric with respect to the If \( f \) is an odd function, then \( f(-x)= \) \( \begin{array}{l}x(x) . \\ -f(x)\end{array} \)
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If \( f \) is an odd function, then \( f(-x) = -f(x) \). This means that for every point on the graph at \( (x, f(x)) \), there is a corresponding point at \( (-x, -f(x)) \) which reflects across the origin. This property is what makes odd functions unique and intriguing! The graph of an odd function is symmetric with respect to the origin. If you were to rotate the graph 180 degrees around the origin, it would look unchanged! This characteristic helps in understanding the behavior of various functions, like sine and cubic functions, showcasing their beautiful symmetry in a visually appealing manner.