Analytic geometry | Mathematical analysis
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve. There are three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound. An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞. More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes. Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis. (Wikipedia).
What are asymptotes? How to find them (several examples). 00:00 Intro 00:07 What is an asymptote? 00:36 Three types of asymptote 02:08 Find horizontal asymptotes for rational functions 04:55 Functions with Two horizontal asymptotes 05:50 Find vertical asymptotes 07:24 Find oblique as
From playlist Calculus
Brainstorming: What is an Asymptote?
In this video, we explore what it means for a curve to have an asymptote. We focus on how to determine when a function has a vertical and/or horizontal asymptote. College Algebra homepage: http://webspace.ship.edu/jehamb/calg.html
From playlist College Algebra
Asymptotes | Graphs | Maths | FuseSchool
Asymptotes | Graphs | Maths | FuseSchool What is an asymptote? An asymptote is a line which continually approaches a curve. The curve gets really really really close to the line but it never quite touches it... why? In this video, we learn all about what an asymptote is. SUBSCRIBE to th
From playlist MATHS
Oblique Asymptotes (1 of 3: Comparing with other asymptotes)
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From playlist Further Work with Functions (related content)
What is a horizontal asymptote
👉 Learn all about asymptotes of a rational function. A rational function is a function, having a variable in the denominator. An asymptote is a line that the graph of a function approaches but never touches. There are the vertical, the horizontal and the slant/oblique asymptotes. The ver
From playlist Asymptotes of Rational Functions | Learn About
👉 Learn all about asymptotes of a rational function. A rational function is a function, having a variable in the denominator. An asymptote is a line that the graph of a function approaches but never touches. There are the vertical, the horizontal and the slant/oblique asymptotes. The ver
From playlist Asymptotes of Rational Functions | Learn About
Overview of asymptotes of a rational function, vertical horizontal and slant
👉 Learn all about asymptotes of a rational function. A rational function is a function, having a variable in the denominator. An asymptote is a line that the graph of a function approaches but never touches. There are the vertical, the horizontal and the slant/oblique asymptotes. The ver
From playlist Asymptotes of Rational Functions | Learn About
From playlist A. Introduction to Calculus
Graphing Rational Functions (Precalculus - College Algebra 44)
Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com How to efficiently sketch rational functions by using Horizontal Asymptotes, Vertical Asymptotes, Oblique Asymptotes, End Behavior, X-Intercepts, Y-Intercept, and select point
From playlist Precalculus - College Algebra/Trigonometry
Graphing Rational Functions Using Transformations With Vertical and Horizontal Asymptotes
This algebra video tutorial explains how to graph rational functions using transformations. It explains how to identify the vertical asymptotes and horizontal asymptotes of the rational function. In addition, it explains how to determine the domain and range of the rational function. It
From playlist New Calculus Video Playlist
Graph Rational Functions | Rational Functions | Pre-Calculus
Let's discover how to identify the asymptotes and intercepts of a rational function. We will begin graphing the reciprocal function and use that to help us understand the asymptotes and intercepts of any reciprocal function. I make short, to-the-point online math tutorials. I struggled w
From playlist Pc - In the classroom
Graphing Rational Functions with Transformations (Precalculus - College Algebra 39)
Support: https://www.patreon.com/ProfessorLeonard Professor Leonard Merch: https://professor-leonard.myshopify.com How to graph rational functions with transformations by considering two basic graphs. Emphasis is placed on finding vertical asymptotes and accurately determining their multi
From playlist Precalculus - College Algebra/Trigonometry
Multiple Examples to find all the asymptotes and intercepts of rational functions
I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. If I helped you in this video, I would love to have you subscribe. My subscribers are my
From playlist Pc Simplified - Rational Functions
Applied Calc 1 Ep 22: Curve sketching
Episode 22 of my videos for my Applied Calculus 1 course at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is about curve sketching. Class webpage: http://cstaecker.fairfield.edu/~cstaecke
From playlist Math 1121 (Applied Calculus 1)
Applied Calc 1 Ep 23: Curve sketching with asymptotes
Episode 23 of my videos for my Applied Calculus 1 course at Fairfield University. This is a first calculus course for undergraduates, taken mostly by business and health/life sciences students. This episode is more curve sketching! Class webpage: http://cstaecker.fairfield.edu/~cstaecker
From playlist Math 1121 (Applied Calculus 1)
When do we have an oblique, slant asymptote for a rational function
👉 Learn all about asymptotes of a rational function. A rational function is a function, having a variable in the denominator. An asymptote is a line that the graph of a function approaches but never touches. There are the vertical, the horizontal and the slant/oblique asymptotes. The ver
From playlist Asymptotes of Rational Functions | Learn About