Asymptote Formula
Various asympote formulas are:
- Horizontal Asymptote Formula
- Vertical Asymptote Formula
- Oblique Asymptote Formula
Let’s learn about them,
Horizontal Asymptote Formula
Horizontal asymptotes are located where the curve approaches a constant value b as x approaches infinity (or negative infinity).
If f (x) = (axm +…)/(bxn +..) is a curve, its horizontal asymptotes are as follows:
- If m < n, then the horizontal asymptote is y = 0, as x tends to infinity, i.e., limx⇢∞ f(x) = 0.
- If m = n, then the horizontal asymptote is y = a/b, as x tents to infinity, i.e., limx⇢∞ f(x) = a/b.
- If m > n, then the f(x) does not have a horizontal asymptote. limx⇢∞ f(x) = ±∞.
Vertical Asymptote Formula
A vertical asymptote is located when the curve shifts in the direction of infinity when x approaches a constant value c from the right or left.
So, to find the vertical asymptote of a function, its denominator must be equated to zero, as a function is undefined when its denominator is zero.
Oblique Asymptote Formula
An oblique asymptote occurs when the curve travels in the direction of the line y = mx + b while x also goes towards infinity in any direction.
Consider the function f(x) = p(x)/q(x), with p(x) and q(x) being polynomials. The given function will have an oblique asymptote only if the degree of the numerator is greater than the denominator.
We get f(x) = {a(x) + r(x)}/q(x) by performing polynomial division on the given function, where a(x) is the quotient and r(x) is the reminder. Now, the oblique asymptote of the given function is a(x).
Asymptote Formula
In geometry, an asymptote is a straight line that approaches a curve on the graph and tends to meet the curve at infinity. An asymptote is a line that a graph of a function approaches but never touches or crosses as it extends towards infinity or a specific point. Asymptotes help to describe the behaviour of functions, particularly their end behaviour and behaviour near undefined points.
In this article, we have covered the asymptote definition, types, formulas, examples and others in detail.
Table of Content
- What is an Asymptote?
- Types of Asymptotes
- Asymptote Formula
- Asymptotes of Hyperbola
- Difference Between Horizontal and Vertical Asymptotes