GMAT GRE 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th grade math 8th grade math 9th grade math 10th grade math 11th grade math 12th grade math Precalculus Worksheets Chapter wise Test MCQ's Math Dictionary Graph Dictionary Multiplicative tables Math Teasers NTSE Chinese Numbers CBSE Sample Papers 
How to find horizontal AsymptotesHow to find horizontal Asymptotes?A horizontal asymptotes is a horizontal line that tells us how the function will behave at every edges of the graph. A function is an equation how two things are related with each other.In general the function tells us how Y is related to X.Usually the functions are often graphed for visualization. The horizontal asymptotes are parallel to Xaxis some times it crosses or cuts the graph. Horizontal asymptotes exists when the numerator and denominator of the function is a polynomials. So we called these functions as rational expressions. Steps for how to find Horizontal Asymptotes1) Write the given equation in y = form.2) If there are factors given in the numerator and denominator then multiply them and write it in the form of polynomial. 3) Check the degree of numerator and denominator. 4) If the degrees are same then horizontal asymptote $y=\frac{(numerator's leading coefficient)}{ (denominator's leading coefficient)}$ 5) If the degree of the denominator greater than the degree of numerator then the horizontal asymptote y = 0 which is nothing but the Xaxis. Examples : 1) Find the horizontal asymptote of the rational function $f(x)=\frac{3x^25x}{x^25x + 6} $ Solution: First we will write the given function in y form. $y = f(x)=\frac{3x^25x}{x^25x + 6} $ Now we will check the degree of numerator and denominator. Degree of numerator = 2 and the degree of the denominator =2 . Both the degrees are same so horizontal asymptote is given by the formula $y=\frac{(numerator's leading coefficient)}{ (denominator's leading coefficient)}$ Numerator's leading coefficient = 3 and denominator's leading coefficient = 1 So the horizontal asymptote is $y =\frac{3}{ 1}$ 2) $f(x)=\frac{x^35}{x6} $ Solution : First we will write the given function in y form. $y= f(x)=\frac{x^35}{x6} $ Now we will check the degree of numerator and denominator. Degree of numerator = 3 and the degree of the denominator =1 . Both the degrees are different so there is no horizontal asymptote. There is a slant asymptote, that you will learn in the next topic. 3) $f(x)=\frac{x8}{x^31}$ Solution : First we will write the given function in y form. $y= f(x)=\frac{x 8}{x^31} $ Now we will check the degree of numerator and denominator. Degree of numerator = 1 and the degree of the denominator = 3 Since the degree of numerator is less than the degree of denominator. So the horizontal asymptote is y = 0. 4) Find the horizontal asymptote from the given graph. Solution : From the graph, we observe that the horizontal asymptote is at y = 2. Practice QuestionsQ.1 Find the horizontal asymptote of the following function.1) $f(x)=\frac{4x^3}{x^24x+2}$ 2) $f(x)=\frac{7x + 2}{x+2}$ 3) $f(x)=\frac{4x + 2}{x^2  5}$ Precalculus Home Covid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Covid19 has affected physical interactions between people. Don't let it affect your learning.
More To Explore
