An odd function is a type of mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. This means that if you take the negative of the input, the output will also be the negative of the original output. Graphically, odd functions are symmetric about the origin, which means that if you rotate the graph 180 degrees around the origin, it looks the same. Common examples of odd functions include the sine function and cubic functions. For instance, the function f(x) = x^3 is odd because f(-x) = -x^3 = -f(x) . Understanding odd functions is important in various fields of mathematics, including calculus and algebra, as they exhibit unique properties that can simplify problem-solving.