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 $(a,\infty)$ for some real number $a$ or an interval of the form $(-\infty,b)$ 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:

$\! \lim_{x \to \infty} f(x) = L, \qquad \lim_{x \to -\infty} f(x) = L$

Related notions

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