The function y = k/x: properties and graph

The function y = k/x (k ≠ 0) is defined for every x except 0, and its values are also nonzero. Its graph is called a hyperbola and consists of two branches. If k > 0, the branches lie in quadrants I and III, and the function decreases on each of the intervals x < 0 and x > 0. If k < 0, the branches lie in quadrants II and IV and the function increases on each of these intervals. The function is odd: replacing x by -x changes the sign of y, so the graph is symmetric about the origin. Since xy = k at every point, x and y are inversely proportional quantities.