Asymptote/Examples/(x + 3) over (x + 2) (x - 1)

Examples of Asymptotes

Asymptotes ($\color { red } {\text {red} }$) to $\dfrac {x + 3} {\paren {x + 2} \paren {x - 1} }$ ($\color { blue } {\text {blue} }$)

Consider the curve whose equation in the Cartesian plane is given by:

$y = \dfrac {x + 3} {\paren {x + 2} \paren {x - 1} }$

This has $2$ vertical asymptotes:

the straight line $x = -2$

the straight line $x = 1$

and $1$ horizontal asymptote:

the straight line $y = 0$.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): asymptote
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): asymptote