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How To Find Horizontal Asymptotes?

by Rudresh Ratnaparkhe
How To Find Horizontal Asymptotes

If you don’t know how to find horizontal asymptotes then don’t worry let me help you with it. I will tell you about how you can find the asymptotes in horizontal in detail. I will describe every important bit of information about how to find the horizontal asymptotes here. Some of the common doubts like how to find vertical and horizontal asymptotes, how to find horizontal asymptotes of an equation, etc will be discussed in this article. So let us begin with how to find horizontal asymptotes.

How To Find Horizontal Asymptotes?

To find horizontal asymptotes you need to first understand what are they. So for your information horizontal asymptotes are the lines drawn horizontally on the graph. To find horizontal asymptotes you will need the following horizontal asymptote rules.

  • If the denominator’s degree that is the largest exponent is greater than the numerator’s degree, then the x-axis is the horizontal asymptote (y = 0).
  • If the numerator degree is greater than the denominator, the horizontal asymptote is not present.
  • If the numerator and denominator degrees are the same, the horizontal asymptote equals the numerator’s leading coefficient that is the largest exponent coefficient is divided by the denominator’s leading coefficient.

How To Find Horizontal Asymptotes Of Different Functions?

Below we have explained information on how to find horizontal asymptotes of a function such as logarithmic, exponential, etc.

How To Find Horizontal Asymptotes Of A Rational Function?

You can find rational function horizontal asymptotes depending on how the degrees of the polynomials in the function numerator and denominator compare. Read below to understand the procedure used to find the horizontal asymptote changes.

  1. If both polynomials are of the same degree, divide the coefficients between the terms of the highest degree.
  2. If the polynomial is smaller than the denominator in the numerator, then the horizontal asymptote is the x-axis (y = 0).
  3. If the polynomial is a greater degree than the denominator in the numerator, then there is no horizontal asymptote.

How To Find Horizontal Asymptotes Of Exponential Functions?

To find exponential horizontal asymptotes functions is very simple. A random line that closely approaches a curve. Vertical, oblique, or horizontal can be an asymptote. Horizontal asymptotes equate with the value reached by the curve as x gets very high or very small. The function y = bx takes only positive values and the horizontal asymptote is the x-axis.

How To Find Horizontal Asymptotes Using Limits?

To find horizontal asymptotes using limits is done as follows

If  limx→∞f(x) = L  or  limx→−∞f(x) = L ,then  y = L  is a horizontal asymptote of  f .

How To Find Horizontal Asymptotes If Degrees Are Equal?

Finding horizontal asymptotes if degrees are equal is simple. If the numerator and denominator are equal in degree, the ratio of leading coefficients is always the horizontal asymptote. Therefore, if the numerator’s leading coefficient is a and that of the denominator is b, the asymptote is the line y = a/b.

How To Find Horizontal Asymptotes On A Graph?

You can find horizontal asymptotes on a graph if the x-axis, or y=0 when the degree of the numerator of a rational function is less than the degree of the denominator. There is no horizontal asymptote when the degree of the numerator of a rational function is greater than that of the denominator. You can also use desmos for how to find horizontal asymptotes calculus to calculate it.

FAQ

How Do You Find The Horizontal Asymptote Of A Function?

To find the horizontal asymptote of a function you will need to check the following things:

  1. If both polynomials are of the same degree, divide the coefficients between the terms of the highest degree.
  2. If the polynomial is smaller than the denominator in the numerator, then the horizontal asymptote is the x-axis (y = 0).
  3. If the polynomial is a greater degree than the denominator in the numerator, then there is no horizontal asymptote.

How Do U Find Horizontal And Vertical Asymptotes?

Below you will know how to find horizontal asymptotes and vertical asymptotes:

Vertical Asymptotes

The line which is vertical where, x = a is called a vertical asymptote of the graph of y = f(x) if,

limx→a− f(x) = ∞, limx→a−f(x) = −∞, limx→a+f(x) = ∞, or limx→a+f(x) = −∞. and,

Horizontal Asymptotes

The line which is horizontal where, y = b is called a horizontal asymptote of the graph of

y = f(x) if either,

limx→∞ f(x) = b or lim x→−∞ f(x) = b.

  • There can be an infinite amount of vertical asymptotes in a graph, but it can only have a maximum of two horizontal asymptotes.
  • The left and right-hand behavior of the graph is represented by horizontal asymptotes.
  • A graph most of the time will never hit a vertical asymptote, but a graph can cross a horizontal asymptote.

What Is The Rule For Horizontal Asymptote?

Below are horizontal asymptote rules, that you can read as follows:

  1. When n is lower than m, y = 0, or the x-axis is the horizontal asymptote. 
  2. When n is equal to m, then y = a/b is equal to the horizontal asymptote. 
  3. If n is greater than m, the horizontal asymptote is not present.

What Is The Easiest Way To Find Asymptotes?

The easiest way to find asymptotes can do it by following ways:

  • Simply set the denominator equal to 0 to find the vertical asymptotes of a rational function and solve for x. 
  • Set and solve the denominator equal to 0: this quadratic can be solved most conveniently by factoring the trinomial and setting the factors equal to 0. 
  • If the numerator degree is less than the denominator degree: horizontal asymptote at y = 0. 
  • If the numerator degree is greater than the denominator degree by one then no horizontal asymptote and slant asymptote.

Conclusion

Above you read about how to find horizontal asymptotes with complete details. I described how you can find the horizontal asymptotes in different ways. You learned about the asymptotes that are horizontal and how the functions, graphs are there to solve them. You saw about the rules of the horizontal asymptotes. I answered few common queries that many people have about asymptotes. This article explained good details on how to find horizontal asymptotes and was helpful for you.

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