An asymptote of a graph is an imaginary line that the graph gets close to as $x$ goes to plus or minus infinity or a particular number. For example, the graph of the rational function $f(x)=\frac{1}{x}$ has two asymptotes — the $x\text{-}$axis and the $y\text{-}$axis.

Analyzing the diagram, the following can be observed.

• As $x$ approaches infinity and as $x$ approaches negative infinity, the value of the function approaches $0.$ Therefore, $y=0,$ or the $x\text{-}$axis, is a horizontal asymptote of the graph of $f.$
• As $x$ approaches $0,$ the value of the function approaches either positive or negative infinity. Therefore, $x=0,$ or the $y\text{-}$axis, is a vertical asymptote of the graph of $f.$

In the coordinate plane below, the asymptotes for three different graphs are shown. The applet demonstrates that asymptotes can be not only vertical and horizontal, but also oblique.