asymptote Definition
- 1a straight line that a curve approaches but never touches as it goes to infinity
- 2a value that a function approaches but never reaches as the input approaches some value
Using asymptote: Examples
Take a moment to familiarize yourself with how "asymptote" can be used in various situations through the following examples!
Example
The curve y = 1/x has two asymptotes, the x-axis and the y-axis.
Example
The function f(x) = 1/x has an asymptote at x = 0.
Example
Asymptotes are important in calculus and the study of functions.
Phrases with asymptote
a horizontal line that a function approaches as the input goes to infinity or negative infinity
Example
The function y = 1/x has a horizontal asymptote at y = 0.
a vertical line that a function approaches as the input approaches some value from the left or right
Example
The function f(x) = 1/(x-2) has a vertical asymptote at x = 2.
a slanted line that a function approaches as the input goes to infinity or negative infinity
Example
The function y = x/(x+1) has an oblique asymptote at y = x.
Origins of asymptote
from Greek 'asumptotos', meaning 'not falling together'
Summary: asymptote in Brief
'Asymptote' [ˈæsɪmptoʊt] refers to a straight line that a curve approaches but never touches as it goes to infinity, or a value that a function approaches but never reaches as the input approaches some value. Asymptotes are important in calculus and the study of functions. Types of asymptotes include horizontal, vertical, and oblique asymptotes.
