Asymptotes

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An asymptote is a line that a curve approaches as it moves closer to infinity. Very commonly the asymptotes of a graph are the $x$ and $y$ axes.

There are three types of asymptotes: horizontal, vertical, and oblique. The x-axis is a horizontal asymptote, the y-axis is a vertical one, while oblique asymptotes are basically diagonal lines in a plane.

The distance between a curve and an asymptote approaches $0$ as they head towards infinity. The graph of a horizontal asymptote is given as $x = a$, while the graph of a vertical asymptote is given as $y = b$. Oblique asymptotes are given by the slope-intercept equation, $y = mx + b$.

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