Vertical,
Horizontal, and Slant Asymptotes
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In a Nut Shell: An asymptote is a line that a curve, f(x),
approaches at a specified point,
such as x = a or as x approaches
± ∞ . There are three types of asymptotes including a vertical, a horizontal, and a
slant asymptote. They are useful in graphing curves. |
|
The line x
= a is a vertical
asymptote of the curve y = f(x)
provided that either lim f(x) = ±
∞ or lim
f(x) =
± ∞ x → a- x → a+ For f(x)
shown in the figure below, there is a vertical asymptote at x = a. |
|
The line y
= L is a horizontal
asymptote of the curve y = f(x)
provided that either lim
f(x) =
L or lim f(x) = L x
→ +∞ x → -∞ For f(x)
shown in the figure below, there is a horizontal asymptote at y
= L |
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Click here to continue
with discussion of asymptotes. |
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