An asymptote of a function is a line that the function's graph approaches as the distance to the origin approaches infinity. As an example, the rational function f(x)=x1 has two asymptotes, the x-axis and the y-axis.
As x→∞ and as x→-∞, the function value approaches 0. Thus, the x-axis, y=0, is a horizontal asymptote of f. Similarly, as x→0, the function value approaches either positive or negative infinity. This means that the y-axis, x=0, is a vertical asymptote of f.