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\n<\/p><\/div>"}. Given a rational function, we can identify the vertical asymptotes by following these steps: Step 1: Factor the numerator and denominator. For the purpose of finding asymptotes, you can mostly ignore the numerator. Get help from our expert homework writers! In this wiki, we will see how to determine horizontal and vertical asymptotes in the specific case of rational functions. We're on this journey with you!About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. Factor the denominator of the function. By using our site, you agree to our. However, it is also possible to determine whether the function has asymptotes or not without using the graph of the function. The asymptotes of a function can be calculated by investigating the behavior of the graph of the function. Since it is factored, set each factor equal to zero and solve. You're not multiplying "ln" by 5, that doesn't make sense. Recall that a polynomial's end behavior will mirror that of the leading term. If the centre of a hyperbola is (x0, y0), then the equation of asymptotes is given as: If the centre of the hyperbola is located at the origin, then the pair of asymptotes is given as: Let us see some examples to find horizontal asymptotes. How to convert a whole number into a decimal? So, vertical asymptotes are x = 1/2 and x = 1. Find the vertical asymptotes by setting the denominator equal to zero and solving for x. When the numerator and denominator have the same degree: Divide the coefficients of the leading variables to find the horizontal asymptote. We can find vertical asymptotes by simply equating the denominator to zero and then solving for Then setting gives the vertical asymptotes at. Learn about finding vertical, horizontal, and slant asymptotes of a function. Our math homework helper is here to help you with any math problem, big or small. So, vertical asymptotes are x = 3/2 and x = -3/2. What are some Real Life Applications of Trigonometry? This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\n<\/p><\/div>"}. Asymptote. New user? Also, since the function tends to infinity as x does, there exists no horizontal asymptote either. Find the vertical and horizontal asymptotes of the functions given below. Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x), How to find root of a number by division method, How to find the components of a unit vector, How to make a fraction into a decimal khan academy, Laplace transform of unit step signal is mcq, Solving linear systems of equations find the error, What is the probability of drawing a picture card. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\u00a9 2023 wikiHow, Inc. All rights reserved. Verifying the obtained Asymptote with the help of a graph. So, vertical asymptotes are x = 4 and x = -3. An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. Can a quadratic function have any asymptotes? As x or x -, y does not tend to any finite value. degree of numerator < degree of denominator. In a rational function, an equation with a ratio of 2 polynomials, an asymptote is a line that curves closely toward the HA. In other words, such an operator between two sets, say set A and set B is called a function if and only if it assigns each element of set B to exactly one element of set A. Find the vertical asymptotes of the rational function $latex f(x)=\frac{{{x}^2}+2x-3}{{{x}^2}-5x-6}$. Here is an example to find the vertical asymptotes of a rational function. MY ANSWER so far.. 34K views 8 years ago. Find the horizontal and vertical asymptotes of the function: f(x) = x2+1/3x+2. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptotes are x = -2, x = 1, and x = 3. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. MAT220 finding vertical and horizontal asymptotes using calculator. 237 subscribers. Find the horizontal asymptotes for f(x) = x+1/2x. If the degree of the numerator is exactly one more than the degree of the denominator, then the graph of the rational function will be roughly a sloping line with some complicated parts in the middle. How to find the horizontal asymptotes of a function? In the above exercise, the degree on the denominator (namely, 2) was bigger than the degree on the numerator (namely, 1), and the horizontal asymptote was y = 0 (the x-axis).This property is always true: If the degree on x in the denominator is larger than the degree on x in the numerator, then the denominator, being "stronger", pulls the fraction down to the x-axis when x gets big. If then the line y = mx + b is called the oblique or slant asymptote because the vertical distances between the curve y = f(x) and the line y = mx + b approaches 0.. For rational functions, oblique asymptotes occur when the degree of the numerator is one more than the . Step 3: If either (or both) of the above limits are real numbers then represent the horizontal asymptote as y = k where k represents the . If. Lets look at the graph of this rational function: We can see that the graph avoids vertical lines $latex x=6$ and $latex x=-1$. Take a look at these pages: Jefferson is the lead author and administrator of Neurochispas.com. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. A quadratic function is a polynomial, so it cannot have any kinds of asymptotes. The calculator can find horizontal, vertical, and slant asymptotes. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. //]]>. With the help of a few examples, learn how to find asymptotes using limits. Find the vertical asymptotes of the graph of the function. The asymptote finder is the online tool for the calculation of asymptotes of rational expressions. window.__mirage2 = {petok:"oILWHr_h2xk_xN1BL7hw7qv_3FpeYkMuyXaXTwUqqF0-31536000-0"}; Step 2: Find lim - f(x). An asymptote is a line that a curve approaches, as it heads towards infinity:. Include your email address to get a message when this question is answered. Don't let these big words intimidate you. The interactive Mathematics and Physics content that I have created has helped many students. Problem 4. Your Mobile number and Email id will not be published. Horizontal asymptotes can occur on both sides of the y-axis, so don't forget to look at both sides of your graph. How to find the oblique asymptotes of a function? Courses on Khan Academy are always 100% free. In order to calculate the horizontal asymptotes, the point of consideration is the degrees of both the numerator and the denominator of the given function. function-asymptotes-calculator. Given a rational function, we can identify the vertical asymptotes by following these steps: Step 1:Factor the numerator and denominator. Asymptote Calculator. The method opted to find the horizontal asymptote changes involves comparing the, in the numerator and denominator of the function. Asymptote Calculator. Step II: Equate the denominator to zero and solve for x. How many whole numbers are there between 1 and 100? Step 2: Observe any restrictions on the domain of the function. Degree of the numerator = Degree of the denominator, Kindly mail your feedback tov4formath@gmail.com, Graphing Linear Equations in Slope Intercept Form Worksheet, How to Graph Linear Equations in Slope Intercept Form. For example, with \( f(x) = \frac{3x}{2x -1} ,\) the denominator of \( 2x-1 \) is 0 when \( x = \frac{1}{2} ,\) so the function has a vertical asymptote at \( \frac{1}{2} .\), Find the vertical asymptote of the graph of the function, The denominator \( x - 2 = 0 \) when \( x = 2 .\) Thus the line \(x=2\) is the vertical asymptote of the given function. Learning to find the three types of asymptotes. In this article, we will see learn to calculate the asymptotes of a function with examples. x 2 5 x 2 + 5 x {\displaystyle {\frac {x-2} {5x^ {2}+5x}}} . Since we can see here the degree of the numerator is less than the denominator, therefore, the horizontalasymptote is located at y = 0. Step 2: Click the blue arrow to submit and see the result! Also, since the function tends to infinity as x does, there exists no horizontal asymptote either. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e5\/Find-Horizontal-Asymptotes-Step-1-Version-2.jpg\/v4-460px-Find-Horizontal-Asymptotes-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/e\/e5\/Find-Horizontal-Asymptotes-Step-1-Version-2.jpg\/v4-728px-Find-Horizontal-Asymptotes-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":" \u00a9 2023 wikiHow, Inc. All rights reserved. \( x^2 - 25 = 0 \) when \( x^2 = 25 ,\) that is, when \( x = 5 \) and \( x = -5 .\) Thus this is where the vertical asymptotes are. \(_\square\). A horizontal asymptote is a horizontal line that a function approaches as it extends toward infinity in the x-direction. Find all three i.e horizontal, vertical, and slant asymptotes There are three types: horizontal, vertical and oblique: The direction can also be negative: The curve can approach from any side (such as from above or below for a horizontal asymptote), To calculate the asymptote, you proceed in the same way as for the crooked asymptote: Divides the numerator by the denominator and calculates this using the polynomial division . wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. Since the function is already in its simplest form, just equate the denominator to zero to ascertain the vertical asymtptote(s). Since they are the same degree, we must divide the coefficients of the highest terms. The graphed line of the function can approach or even cross the horizontal asymptote. If the degree of the polynomials both in numerator and denominator is equal, then divide the coefficients of highest degree terms to get the horizontal asymptotes. then the graph of y = f (x) will have a horizontal asymptote at y = a n /b m. For everyone. [3] For example, suppose you begin with the function. If f (x) = L or f (x) = L, then the line y = L is a horiztonal asymptote of the function f. For example, consider the function f (x) = . How many types of number systems are there? This article was co-authored by wikiHow staff writer, Jessica Gibson. This image may not be used by other entities without the express written consent of wikiHow, Inc. \u00a9 2023 wikiHow, Inc. All rights reserved. To find the horizontal asymptotes, check the degrees of the numerator and denominator. This article has been viewed 16,366 times. Degree of numerator is less than degree of denominator: horizontal asymptote at. This is where the vertical asymptotes occur. Hence, horizontal asymptote is located at y = 1/2, Find the horizontal asymptotes for f(x) = x/x2+3. What is the probability of getting a sum of 7 when two dice are thrown? An asymptote is a horizontal/vertical oblique line whose distance from the graph of a function keeps decreasing and approaches zero, but never gets there. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam. Really good app helps with explains math problems that I just cant get, but this app also gives you the feature to report any problem which is having incorrect steps or the answer is wrong. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.For free. i.e., apply the limit for the function as x. To justify this, we can use either of the following two facts: lim x 5 f ( x) = lim x 5 + f ( x) = . Now that the function is in its simplest form, equate the denominator to zero in order to determine the vertical asymptote. Examples: Find the horizontal asymptote of each rational function: First we must compare the degrees of the polynomials. Since it is factored, set each factor equal to zero and solve. Since the highest degree here in both numerator and denominator is 1, therefore, we will consider here the coefficient of x. While vertical asymptotes describe the behavior of a graph as the output gets very large or very small, horizontal asymptotes help describe the behavior of a graph as the input gets very large or very small. This is a really good app, I have been struggling in math, and whenever I have late work, this app helps me! Since the degree of the numerator is greater than that of the denominator, the given function does not have any horizontal asymptote. Algebra. Step 1: Simplify the rational function. An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. Some curves have asymptotes that are oblique, that is, neither horizontal nor vertical. The method for calculating asymptotes varies depending on whether the asymptote is vertical, horizontal, or oblique. To find the horizontal asymptotes, check the degrees of the numerator and denominator. The vertical asymptote is a vertical line that the graph of a function approaches but never touches. Here are the rules to find asymptotes of a function y = f (x). You can learn anything you want if you're willing to put in the time and effort. Step 2: Set the denominator of the simplified rational function to zero and solve. The distance between the curve and the asymptote tends to zero as they head to infinity (or infinity), as x goes to infinity (or infinity) the curve approaches some constant value b. as x approaches some constant value c (from the left or right) then the curve goes towards infinity (or infinity). Piecewise Functions How to Solve and Graph. Solution:We start by factoring the numerator and the denominator: $latex f(x)=\frac{(x+3)(x-1)}{(x-6)(x+1)}$. Start practicingand saving your progressnow: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:r. In the above example, we have a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. 2.6: Limits at Infinity; Horizontal Asymptotes. The graph of y = f(x) will have vertical asymptotes at those values of x for which the denominator is equal to zero. Log in. For example, with \( f(x) = \frac{3x^2 + 2x - 1}{4x^2 + 3x - 2} ,\) we only need to consider \( \frac{3x^2}{4x^2} .\) Since the \( x^2 \) terms now can cancel, we are left with \( \frac{3}{4} ,\) which is in fact where the horizontal asymptote of the rational function is. Problem 6. Start practicingand saving your progressnow: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:graphs-of-rational-functions/v/finding-asymptotes-exampleAlgebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. Solving Cubic Equations - Methods and Examples. The user gets all of the possible asymptotes and a plotted graph for a particular expression. Hence,there is no horizontal asymptote. \(\begin{array}{l}\lim_{x\rightarrow -a-0}f(x)=\lim_{x\rightarrow -1-0}\frac{3x-2}{x+1} =\frac{-5}{-0}=+\infty \\ \lim_{x\rightarrow -a+0}f(x)=\lim_{x\rightarrow -1+0}\frac{3x-2}{x+1} =\frac{-5}{0}=-\infty\end{array} \). x2 + 2 x - 8 = 0. Problem 7. When one quantity is dependent on another, a function is created. y =0 y = 0. Learn how to find the vertical/horizontal asymptotes of a function. In the numerator, the coefficient of the highest term is 4. Need help with math homework? Also, rational functions and the rules in finding vertical and horizontal asymptotes can be used to determine limits without graphing a function. Degree of the denominator > Degree of the numerator. To find the horizontal asymptotes apply the limit x or x -. ( x + 4) ( x - 2) = 0. x = -4 or x = 2. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image may not be used by other entities without the express written consent of wikiHow, Inc. \u00a9 2023 wikiHow, Inc. All rights reserved. The highest exponent of numerator and denominator are equal. The vertical line x = a is called a vertical asymptote of the graph of y = f(x) if. then the graph of y = f (x) will have no horizontal asymptote. Therefore, we draw the vertical asymptotes as dashed lines: Find the vertical asymptotes of the function $latex g(x)=\frac{x+2}{{{x}^2}+2x-8}$. A logarithmic function is of the form y = log (ax + b). The equation of the asymptote is the integer part of the result of the division. As you can see, the degree of the numerator is greater than that of the denominator. The horizontal asymptote identifies the function's final behaviour. To find a horizontal asymptote, compare the degrees of the polynomials in the numerator and denominator of the rational function. This function can no longer be simplified. Except for the breaks at the vertical asymptotes, the graph should be a nice smooth curve with no sharp corners. then the graph of y = f(x) will have a horizontal asymptote at y = 0 (i.e., the x-axis). A graph will (almost) never touch a vertical asymptote; however, a graph may cross a horizontal asymptote. For example, if we were to have a logistic function modeling the spread of the coronavirus, the upper horizontal asymptote (limit as x goes to positive infinity) would probably be the size of the Earth's population, since the maximum number of people that . ), A vertical asymptote with a rational function occurs when there is division by zero. I love this app, you can do problems so easily and learn off them to, it is really amazing but it took a long time before downloading. These questions will only make sense when you know Rational Expressions. Since the degree of the numerator is equal to that of the denominator, the horizontal asymptote is ascertained by dividing the leading coefficients. Courses on Khan Academy are always 100% free. The question seeks to gauge your understanding of horizontal asymptotes of rational functions. Find a relation between x and y if the point (x, y) is equidistant from (3, 6) and (-3, 4), Let z = 8 + 3i and w = 7 + 2i, find z/w and z.w, Find sin2x, cos2x, and tan2x from the given information: cosec(x) = 6, and tan (x) < 0, If tan (A + B) = 3 and tan (A B) = 1/3, 0 < A + B 90; A > B, then find A and B, If sin (A B) = 1/2, cos (A + B) = 1/2, and 0. This image may not be used by other entities without the express written consent of wikiHow, Inc. \u00a9 2023 wikiHow, Inc. All rights reserved. In the following example, a Rational function consists of asymptotes. Oblique Asymptote or Slant Asymptote. or may actually cross over (possibly many times), and even move away and back again. Therefore, the function f(x) has a horizontal asymptote at y = 3. How to Find Vertical & Horizontal Asymptotes We can find vertical asymptotes by simply equating the denominator to zero and then solving for Then setting gives the vertical asymptotes at Figure out mathematic question. Figure 4.6.3: The graph of f(x) = (cosx) / x + 1 crosses its horizontal asymptote y = 1 an infinite number of times. The ln symbol is an operational symbol just like a multiplication or division sign. Log in here. The given function is quadratic. Since the function is already in its simplest form, just equate the denominator to zero to ascertain the vertical asymptote(s). en. So, you have a horizontal asymptote at y = 0. This occurs becausexcannot be equal to 6 or -1. . Explain different types of data in statistics, Difference between an Arithmetic Sequence and a Geometric Sequence. Level up your tech skills and stay ahead of the curve. Follow the examples below to see how well you can solve similar problems: Problem One: Find the vertical asymptote of the following function: In this case, we set the denominator equal to zero. When x moves to infinity or -infinity, the curve approaches some constant value b, and is called a Horizontal Asymptote. To find the horizontal asymptotes, we have to remember the following: Find the horizontal asymptotes of the function $latex g(x)=\frac{x+2}{2x}$. 2 3 ( ) + = x x f x holes: vertical asymptotes: x-intercepts: There are three types of asymptotes namely: The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity. The graphed line of the function can approach or even cross the horizontal asymptote. (There may be an oblique or "slant" asymptote or something related. Find the horizontal asymptotes for f(x) =(x2+3)/x+1. It totally helped me a lot. What are the vertical and horizontal asymptotes? But you should really add a Erueka Math book thing for 1st, 2nd, 3rd, 4th, 5th, 6th grade, and more. Problem 3. What is the importance of the number system? For Oblique asymptote of the graph function y=f(x) for the straight-line equation is y=kx+b for the limit x + , if and only if the following two limits are finite. Point of Intersection of Two Lines Formula. Ask here: https://forms.gle/dfR9HbCu6qpWbJdo7Follow the Community: https://www.youtube.com/user/MrBrianMcLogan/community Organized Videos: Find the Asymptotes of Rational Functionshttps://www.youtube.com/playlist?list=PL0G-Nd0V5ZMoQqOMQmtSQRJkXwCeAc0_L Find the Vertical and Horizontal Asymptotes of a Rational Function y=0https://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrCy9FP2EeZRJUlawuGJ0xr Asymptotes of Rational Functions | Learn Abouthttps://www.youtube.com/playlist?list=PL0G-Nd0V5ZMqRIveo9efZ9A4dfmViSM5Z Find the Asymptotes of a Rational Function with Trighttps://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrWuoRiLTAlpeU02mU76799 Find the Asymptotes and Holes of a Rational Functionhttps://www.youtube.com/playlist?list=PL0G-Nd0V5ZMq01KEN2RVJsQsBO3YK1qne Find the Slant Asymptotes of the Rational Functionhttps://www.youtube.com/playlist?list=PL0G-Nd0V5ZMrL9iQ1eA9gWo1vuw-UqDXo Organized playlists by classes here: https://www.youtube.com/user/MrBrianMcLogan/playlists My Website - http://www.freemathvideos.comSurvive Math Class Checklist: Ten Steps to a Better Year: https://www.brianmclogan.com/email-capture-fdea604e-9ee8-433f-aa93-c6fefdfe4d57Connect with me:Facebook - https://www.facebook.com/freemathvideosInstagram - https://www.instagram.com/brianmclogan/Twitter - https://twitter.com/mrbrianmcloganLinkedin - https://www.linkedin.com/in/brian-mclogan-16b43623/ Current Courses on Udemy: https://www.udemy.com/user/brianmclogan2/ About Me: I make short, to-the-point online math tutorials. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. If the degree of the polynomial in the numerator is equal to the degree of the polynomial in the denominator, we divide the coefficients of the terms with the largest degree to obtain the horizontal asymptotes. what is a horizontal asymptote? Jessica Gibson is a Writer and Editor who's been with wikiHow since 2014. Updated: 01/27/2022 A recipe for finding a horizontal asymptote of a rational function: but it is a slanted line, i.e. The criteria for determining the horizontal asymptotes of a function are as follows: There are two steps to be followed in order to ascertain the vertical asymptote of rational functions. The curves approach these asymptotes but never visit them. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. To recall that an asymptote is a line that the graph of a function approaches but never touches. As another example, your equation might be, In the previous example that started with.
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\n<\/p><\/div>"}, How to Find Horizontal Asymptotes: Rules for Rational Functions, https://flexbooks.ck12.org/cbook/ck-12-precalculus-concepts-2.0/section/2.10/primary/lesson/horizontal-asymptotes-pcalc/, https://www.math.purdue.edu/academic/files/courses/2016summer/MA15800/Slantsymptotes.pdf, https://sciencetrends.com/how-to-find-horizontal-asymptotes/. How do I find a horizontal asymptote of a rational function? A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_confirmation=1Support my channel by becoming a member: https://www.youtube.com/channel/UCQv3dpUXUWvDFQarHrS5P9A/joinHave questions? [CDATA[ An asymptote is a line that the graph of a function approaches but never touches. To simplify the function, you need to break the denominator into its factors as much as possible. Horizontal asymptotes. The vertical and horizontal asymptotes of the function f(x) = (3x 2 + 6x) / (x 2 + x) will also be found. It is used in everyday life, from counting to measuring to more complex calculations. How to Find Limits Using Asymptotes. To determine mathematic equations, one must first understand the concepts of mathematics and then use these concepts to solve problems. Find more here: https://www.freemathvideos.com/about-me/#asymptotes #functions #brianmclogan Problem 5. If you see a dashed or dotted horizontal line on a graph, it refers to a horizontal asymptote (HA). A vertical asymptote of a graph is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a. To find the horizontal asymptotes apply the limit x or x -. Two bisecting lines that are passing by the center of the hyperbola that doesnt touch the curve are known as the Asymptotes. Therefore, the function f(x) has a vertical asymptote at x = -1. When graphing a function, asymptotes are highly useful since they help you think about which lines the curve should not cross. What is the probability of getting a sum of 9 when two dice are thrown simultaneously. Graph! If the degree of the numerator is greater than the degree of the denominator, then there are no horizontal asymptotes. The algebraic limit laws and squeeze theorem we introduced in Introduction to Limits also apply to limits at infinity. Jessica also completed an MA in History from The University of Oregon in 2013. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/3e\/Find-Horizontal-Asymptotes-Step-7-Version-2.jpg\/v4-460px-Find-Horizontal-Asymptotes-Step-7-Version-2.jpg","bigUrl":"\/images\/thumb\/3\/3e\/Find-Horizontal-Asymptotes-Step-7-Version-2.jpg\/v4-728px-Find-Horizontal-Asymptotes-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
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