Horizontal asymptote

Definition

For a curve

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For a function

Suppose $f$ is a function whose domain contains an interval of the form $(a,\mathrm{\infty })$ for some real number $a$ or an interval of the form $(-\mathrm{\infty },b)$ for some real number $b$. We say that the line $y=L$ is a horizontal asymptote for the graph of $f$ if one or both of these holds:

$\underset{x\to \mathrm{\infty }}{lim}f(x)=L,\underset{x\to -\mathrm{\infty }}{lim}f(x)=L$

Related notions

• Vertical asymptote
• Oblique asymptote
• Additively asymptotic functions
• Multiplicatively asymptotic functions