a
symp
tote
Plural
asymptotes
1
a straight line that a curve approaches indefinitely but never intersects, characterizing the limiting behavior of the curve
- The hyperbola has asymptotes that represent the lines the curve approaches but never crosses.
- A rational function may have vertical asymptotes where the function approaches infinity.
- A horizontal asymptote occurs when the values of a function approach a constant as the input goes to positive or negative infinity.
- Tangent lines to a curve at infinity can act as asymptotes, describing the curve's behavior.
- Exponential functions may exhibit horizontal asymptotes, indicating stability in the long run.