The reciprocal function is a mathematical function defined as f(x) = \frac1x . This means that for any non-zero input x , the output is the multiplicative inverse of x . The function is undefined at x = 0 because division by zero is not possible. The graph of the reciprocal function consists of two distinct curves, known as hyperbolas, located in the first and third quadrants of the Cartesian plane. The reciprocal function has important properties, such as being an odd function, which means that f(-x) = -f(x) . It also approaches zero as x approaches infinity and becomes infinitely large as x approaches zero from either side. This behavior makes the reciprocal function useful in various fields, including algebra, calculus, and physics.