Asymptote Calculator

A straight line is called an asymptote to the curve y = f (x) if, in layman’s term, the curve touches the line at infinity.

What is Asymptote Calculator?

'Cuemath's Asymptote Calculator' is an online tool that helps to calculate the asymptotic graph for a given function. Cuemath's Asymptote Calculator helps you to find an asymptotic graph for a given function within a few seconds.

How to Use Asymptote Calculator?

Please follow the steps below on how to use the calculator:

• Step1: Enter the function with respect to one variable in the given input boxes.
• Step 2: Click on the "Compute" button to find an asymptotic graph for a given function
• Step 3:  Click on the "Reset" button to clear the fields and find the asymptotic graph for different functions.

How to Find Asymptotes?

An asymptote is defined as a line being approached by a curve but doesn't meet it infinitely or you can say that asymptote is a line to which the curve converges. The asymptote never crosses the curve even though they get infinitely close.

There are three types of asymptotes: 1.Horizontal asymptote 2.Vertical asymptote 3.Slant asymptote

1.Horizontal asymptote: The method to find the horizontal asymptote changes based on the degrees of the polynomials in the numerator and denominator of the function.

• If both the polynomials have the same degree, divide the coefficients of the largest degree terms. This is your asymptote!
• If the degree of the numerator is less than the denominator, then the asymptote is located at y=0.
• If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote! 

2.Vertical asymptote: A vertical asymptote occurs in rational functions at the points when the denominator is zero and the numerator is not equal to zero. We can find the vertical asymptote by equating the denominator of the rational function to zero.

Solved Example:

Find asymptote of given function f(x) = (x + 5) / (x - 3)

Solution : 

To find a vertical asymptote, equate the denominator of the rational function to zero.

x - 3 = 0

x = 3

So, there exists a vertical asymptote at x = 3

\(\lim _{x \rightarrow 3+} f(x)=\pm \infty, \quad \lim _{x \rightarrow 3-} f(x)=\pm \infty\)

In this case, we have the horizontal asymptote at the point y=1 as it falls under case -1. (numerator and denominator are of same degree: linear)

Similarly, you can try the calculator and find the asymptotes for the following:

• (x² + x +1) / (x + 1)
• (x + 5) / ( x - 6)