Vertical Asymptotes - Maple Help

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Vertical Asymptotes

Main Concept

An asymptote is a line that the graph of a function approaches as either x or y approaches infinity. There are three types of asymptotes: vertical, horizontal and oblique.

Vertical Asymptotes

 Vertical Asymptote A vertical asymptote is a vertical line, $x=a$, that has the property that either:   1. 2.   That is, as $x$ approaches $a$ from either the positive or negative side, the function approaches infinity.   Vertical asymptotes occur at the values where a rational function has a denominator of 0. The function is undefined at these points.

Horizontal Asymptotes

 Horizontal Asymptote A horizontal asymptote is a horizontal line, $y=a$, that has the property that either:   1. 2.   Horizontal asymptotes occur when the numerator of a rational function has degree less than or equal to the degree of the denominator. If the denominator has degree $n$, the horizontal asymptote can be calculated by dividing the coefficient of the ${x}^{n}$-th term of the numerator (it may be 0 if the numerator has a smaller degree) by the coefficient of the ${x}^{n}$-th term of the denominator.

Oblique Asymptotes

 Oblique Asymptote An oblique or slant asymptote is an asymptote along a line $y=\mathrm{mx}+b$, where $0<\left|m\right|<\infty$. Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator.

Click or drag to place up to 5 points through which a curve (blue) will be drawn. The $x$-intercepts (green), the reciprocal of the curve (black) and any vertical asymptotes of the reciprocal (magenta) will also be shown.

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