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{{ printedBook.courseTrack.name }} {{ printedBook.name }} 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 $f.$