Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !!
Finding Slant Asymptotes of Rational Functions. In this video, I describe when a rational function has a slant asymptote, briefly describe what a slant asymptote is, and then do two examples.

Views: 406527
patrickJMT

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !!
Finding All Asymptotes of a Rational Function (Vertical, Horizontal, Oblique / Slant).
Here we look at a function and find the vertical asymptote and also conclude that there are no horizontal asymptotes, but that an oblique asymptote does exist. We then use long division to find the oblique asymptote.

Views: 673883
patrickJMT

This algebra video tutorial explains how to identify the horizontal asymptotes and slant asymptotes of rational functions by comparing the degree of the numerator with the degree of the denominator of the rational expression. The equation of the slant asymptote can be determine using long division if the degree of the numerator exceeds the degree of the denominator by exactly 1. This algebra video tutorial contains plenty of examples and practice problems.
New Algebra Playlist:
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Views: 22503
The Organic Chemistry Tutor

This math video tutorial shows you how to find the horizontal, vertical and slant / oblique asymptote of a rational function. This video is for students who might be taking algebra 1 or 2, precalculus or calculus in high school or those who might be taking college algebra in an university. This video contains plenty of notes, examples, and practice problems for you to master the concepts.
Here is a list of topics:
1. Horizontal and Vertical Asymptotes Review
2. Setting the Denominator Equal to Zero to Find The Vertical Asymptote
3. Top Heavy vs Bottom Heavy Functions - Comparing the Degree of The Numerator with the Denominator of the Fraction to Identify the Horizontal Asymptotes
4. Horizontal Asymptotes and End Behavior - As x approaches Infinity
5. Using Long Division To Find The Equation of The Slant / Oblique Asymptote
6. Graphing Rational Functions Using X and Y Intercepts
7. How To Identify and Remove any Holes or Points of Discontinuity
8. Point Discontinuity vs Infinite Discontinuity
9. Domain and Range of Rational Functions
10. Removing the Vertical Asymptote and X Coordinate of the Hole from the Domain
11. Removing the Horizontal Asymptote and Y Coordinate of the Hole from the Range
12. How To Determine / Calculate the X and Y Intercepts of a Rational Expression

Views: 197289
The Organic Chemistry Tutor

This algebra 2 / precalculus video tutorial explains how to graph rational functions with asymptotes and holes. It shows you how to identify the vertical asymptotes by setting the denominator equal to zero and solving for x. It shows you how to find the equation of the horizontal asymptote by comparing the degree of the numerator with that of the denominator. In addition, it shows you how to find and graph the slant asymptote / oblique asymptote using long division. This video also shows you how to identify the x and y coordinate of any holes in the graph. This video contains plenty of examples and practice problems including those in which factoring quadratic expressions and equations are involved. This video also discusses the transformations that occur when graphing rational functions. Horizontal and Vertical shifts are covered as well as reflection over the y axis and the origin. In addition, this video shows you how to the coordinates of the x intercept and y intercept. Finally, this tutorial shows you how to write the domain and range of a rational function using interval notation. It mentions when parentheses and brackets should be use. Whenever you need to write the domain of a rational function, you need to take into account the vertical asymptote and the x coordinate of any holes in the graph. For the range, you need to remove the horizontal asymptote and the y coordinate of any holes in the curve. This video might be useful for students taking calculus.

Views: 141881
The Organic Chemistry Tutor

Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and y-intercepts. After finding the asymptotes and the intercepts, we graph the values and then select some random points usually at each side of the asymptotes and the intercepts and graph the points, this enables us to identify the behavior of the graph and thus enable us to graph the function.
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#rationalfunctions #graphrationalfunctions
#rationalfunctions #graphrationalfunctions

Views: 19695
Brian McLogan

This video explains how to determine slant asymptotes of rational functions.
http://mathispower4u.yolasite.com/

Views: 13201
Mathispower4u

A slant (oblique) asymptote occurs when the polynomial in the numerator is one degree higher than the polynomial in the denominator. This video explains the oblique asymptotes with graph and examples.
Facebook page: https://tinyurl.com/y874hk4b

Views: 1216
InsideMaths

More resources available at www.misterwootube.com

Views: 4725
Eddie Woo

How to find a slant (or oblique) asymptote of a rational function using either synthetic division or algebraic long division. This video is provided by the Learning Assistance Center of Howard Community College. For more math videos and exercises, go to HCCMathHelp.com.

Views: 4148
HCCMathHelp

Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptote(s) of a rational function, we set the denominator equal to 0 and solve for x.
The horizontal asymptote is a horizontal line which the graph of the function approaches but never crosses (though they sometimes cross them). A rational function has a horizontal asymptote of y = 0 when the degree of the numerator is less than the degree of the denominator. A rational function has a horizontal asymptote of y = c, (where c is the quotient of the leading coefficient of the numerator and that of the denominator) when the degree of the numerator is equal to the degree of the denominator. A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.
#rationalfunctions #findasymptotes
#rationalfunctions #findasymptotes
#rationalfunctions #findasymptotes
#graphradicals #findasymptotes

Views: 325263
Brian McLogan

This video show how to find the slant asymptote of a rational function, if one exists.

Views: 1266
George Engel

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Rational Function : Find the Asymptotes (Vertical, Horizontal, Slant / Oblique)

Views: 262651
patrickJMT

FINDING SLANT ASYMPTOTES OF RATIONAL FUNCTIONS (from Unit L Practice Test; content from Unit G)
Covers 4 problems from Unit L Practice Test

Views: 117
Crystal Kirch

This example shows how to find the slant asymptote for a rational function. Remember that a rational function will only have a slant asymptote if the top polynomial Is one degree larger than the bottom polynomial. For more videos please visit http://www.mysecretmathtutor.com

Views: 95145
MySecretMathTutor

This is a video tutorial on how to find the oblique an slant asymptotes for rational expressions. The video covers both techniques of synthetic and polynomial long division. For more math shorts go to www.MathByFives.com
For Math Tee-Shirts go to www.MathByFives.deco-apparel.com

Views: 22757
Mathbyfives

[Maths - 1 , First yr Playlist] https://www.youtube.com/playlist?list=PL5fCG6TOVhr73GZ2jh3QzQ6xDOKeqxtL-
Leibnitz Theorem - Maths Sem 1 https://youtu.be/17xtKImNlMg
Successive Differentiation and Leibnitz Theorem - https://youtu.be/2VpyJXiMkRw
Taylors Theorem and Maclaurin's Theorem https://youtu.be/zFacAUcRydk
Convergent and Divergent Series [Hindi] – Maths https://youtu.be/O99LRM7kXmU
Comparison Test [Hindi] - https://youtu.be/v8OkmP-XNXA
D'Alembert's Ratio Test - https://youtu.be/d3NnvPXZfcE
Raabe's (Higher Ratio) Test - Convergent series https://youtu.be/0t9Gvj8rVMQ
Asymptodes , Oblique Asymptodes - Maths Sem 1 https://youtu.be/lyBL3fCx374

Views: 87419
Study Buddy

This video provides an example of how to determine the equations of the vertical and slant asymptotes of a rational function.
Site: http://mathispower4u.com

Views: 12141
Mathispower4u

Full example of horizontal and slant asymptotes from Educator.com’s Precalculus class. Want more than just one video example? Our full lesson includes in-depth video explanations of finding asymptotes with even more worked out examples. ►See the entire syllabus at https://www.educator.com/mathematics/pre-calculus/selhorst-jones/?utm_source=YT&utm_medium=SEO&utm_campaign=PRECALCYT
In this video, we’ll discuss how to find if there are any horizontal or slant (oblique) asymptotes. We will use long division/ polynomial division to calculate the horizontal and slant asymptote and this will be useful in Precalculus and Math Analysis when studying rational functions.
Like other instructors such as Khan Academy, patrickjmt, ProfRobBob, ThatTutorGuy and MathBFF? Our Precalculus instructor is pretty awesome too. Professor Vincent Selhorst-Jones will make sure you understand every concept and reinforce what you learned through many examples. He has been teaching 8+ years and double-majored in Mathematics and Theater at Pomona College, as well as received an M.F.A. in Acting from Harvard University.
So what are you waiting for? Join over 100K satisfied high school and college students who have aced their classes and exams with https://www.Educator.com’s videos.

Views: 515
Educator.com

This video by Fort Bend Tutoring shows the process of finding and graphing the oblique/slant asymptotes of rational functions. Eight examples are shown in this FBT video. Instruction by Larry "Mr. Whitt" Whittington. Intro/Outro by Chuck Knipp's Shirley Q. Liquor.
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Rational Functions: Domain and Intercepts
https://youtu.be/zjW8ulFu3ek
Vertical Asymptotes
https://youtu.be/p955Tvla-GY
Horizontal Asymptotes
https://youtu.be/eDdlko8cTa4
Holes
https://youtu.be/Gq6fMkDDqdA
Dividing Polynomials
https://youtu.be/AdTRwnyf52c
Graphing Linear Equations: Slope-Intercept Form
https://youtu.be/DVLOvBLaPlQ
Please donate to assist us in bringing the world more free videos through our YouTube Channel using the link: http://www.tutormemath.net/free-tutorials.html
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Views: 12181
Fort Bend Tutoring

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/algebra2/rational-expressions/rational-function-graphing/e/graphs-of-rational-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Watch the next lesson: https://www.khanacademy.org/math/algebra2/rational-expressions/direct_inverse_variation/v/direct-and-inverse-variation?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/rational-expressions/rational-function-graphing/v/finding-asymptotes-example?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. 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. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. 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. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. 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. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Views: 617597
Khan Academy

► My Applications of Derivatives course: https://www.kristakingmath.com/applications-of-derivatives-course
A rational function (which is a fraction in which both the numerator and denominator are polynomials) has a slant asymptote when the degree of the numerator is greater than the degree of the denominator.
To find a slant asymptote, you need to perform polynomial long division. The result of the long division, not including the remainder term, is the slant asymptote of the function.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com
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QUORA // https://www.quora.com/profile/Krista-King

Views: 33069
Krista King

This video demonstrates how to find Horizontal, Vertical, and Slant Asymptotes for Rational Functions.
*******************************************
Don’t forget guys, if you like this video please “Like” and “Share” it with your friends to show your support - it really helps me out!
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For More Math Tutorial Videos, check out all of my Playlists:
TI-84 Calculator Videos: http://bit.ly/2novtib
Calculus Videos: http://bit.ly/2nozSlf
AP Calculus AB Test Tips Videos: http://bit.ly/2noq7DM
STEM Project in Calculus: http://bit.ly/2noq0bq
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Classroom Teaching Ideas: http://bit.ly/2nouxKO
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Be sure to check out Cole’s World of Mathematics around the web!
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Views: 1012
Cole's World of Mathematics

How to determine visually asymptotes from a graph.

Views: 14656
mathlablady1

Learn how to find the slant/oblique asymptotes of a function. A slant (oblique) asymptote usually occurs when the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator. To find the slant asymptote of a rational function, we divide the numerator by the denominator using either long division or synthetic division. The quotient obtained when the numerator is divided by the denominator is the slant asymptote of the function.
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#rationalfunctions #findasymptotes
#rationalfunctions #findasymptotes
#graphradicals #findasymptotes

Views: 17934
Brian McLogan

MIT grad shows how to find the vertical asymptotes of a rational function and what they look like on a graph. To skip ahead: 1) For the STEPS TO FIND THE VERTICAL ASYMPTOTE(S) and an example with two vertical asymptotes, skip to 0:19. 2) For an example in which FACTORS CANCEL and that has one vertical asymptote and a HOLE, skip to 5:58. 3) For an example with NO VERTICAL ASYMPTOTES, skip to time 10:12. Nancy formerly of MathBFF explains the steps.
Follow me on Instagram! https://instagram.com/mathnancy
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For how to find the HORIZONTAL ASYMPTOTE jump to: https://youtu.be/qJrrZQgSkO8
For how to FACTOR quadratics jump to: https://youtu.be/YtN9_tCaRQc
For how to find the DOMAIN of a function jump to: https://youtu.be/GQGFMUfr10M
What is a vertical asymptote? It's an invisible vertical line that a function gets really really close to but never reaches. How do you find the vertical asymptote(s) from the given equation?
THREE STEPS TO FIND THE VERTICAL ASYMPTOTE(S): For a rational function, there are three main steps you can always follow to find all the vertical asymptotes, if there are any:
STEP 1) FACTOR: The first step is to factor the top and bottom (numerator and denominator) if you can, and as much as you can. For instance, in the function f(x) = (x^2 + 3x - 10)/(x^2 - 4), you can factor both the top and bottom. The numerator, x^2 + 3x - 10, is a quadratic that factors into (x + 5)(x - 2), and the denominator, x^2 - 4, is a difference of squares that factors into (x + 2)(x - 2). You then rewrite the whole function with both of these factorizations so that you have f(x) = [(x + 5)(x - 2)] / [(x + 2)(x - 2)].
STEP 2) CANCEL: Next, simplify the function by canceling any factors that are the same on top and bottom. If there are no common factors, you can leave it alone. In our example from Step 1, there is an x - 2 term on both the top and bottom, so we can cancel those two factors. You can rewrite the function after getting rid of those similar factors so that it looks like: f(x) = (x + 5)/(x + 2).
STEP 3) SET THE DENOMINATOR EQUAL TO ZERO: After simplifying and getting rid of any common factors, the last step is to find the real zeros of the denominator by taking the bottom of the simplified function and setting it equal to zero. You then solve that equation for x, and any real numbers you get as a solution for x are where there are vertical asymptotes. You can write your answers as just "x equals [some number]". If you have vertical asymptotes, they will always be in that form, such as x = 3 or x = -2. These represent vertical (invisible) lines on the graph that your function approaches but never crosses.
Remember that if you get an imaginary answer when you solve for x (such as a square root of a negative number), then there are no vertical asymptotes. If there is no real solution when you solve for x, then there are NO VERTICAL ASYMPTOTES. Note: By the way, if you had factors that cancelled in Step 2, that created a "hole", or removable discontinuity, on the graph where the function was indeterminate.
For more of my math videos, check out: http://nancypi.com

Views: 92515
NancyPi

Learn how to find slant asymptotes when graphing rational functions in this free math video tutorial by Mario's Math Tutoring. We go through 2 examples.
0:16 Example 1 Graph f(x) = x^2/(x-2)
0:21 How to Recognize a Slant Asymptote
0:37 How to Do Synthetic Division to Find Equation of Slant Asymptote
1:12 Showing Polynomial Division to Find Slant Asymptote
1:58 Graphing Slant Asymptote
2:22 Graphing Vertical Asymptote
2:38 How to Find the X and Y Intercepts
3:08 Using Sign Analysis to Find the Direction of Graph Near Vertical Asymptotes
4:35 Example 2 Graphing f(x) = x^3/(x^2 - 1)
Related Videos:
Playlist of Videos on Graphing Rational Functions
https://www.youtube.com/playlist?list=PLHRatQsym1_jEZ8u_SDw9TSP_0GqFW5ky
Looking to raise your math score on the ACT and new SAT?
Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale at
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For online 1-to-1 tutoring or more information about me see my website at:
http://www.mariosmathtutoring.com
* Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)
http://www.mariosmathtutoring.com/free-math-videos.html

Views: 1830
Mario's Math Tutoring

In this video, we observe that what we have learned so far in the course is sufficient to show why the remainder must be discarded in finding the oblique (slant) asymptote. We show that, by using limits, and letting x go to infinity, the linear portion of the asymptote expression dominates, even if we take into account the remainder. This means that, for oblique asymptotes, all that matters is the linear part of the expression.
The play list: http://www.youtube.com/playlist?list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6
Synthetic Division with Fractional Zeroes: http://www.youtube.com/watch?v=iK6iS80Mm6c&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=2
Oblique asymptotes and finding them with long division: http://www.youtube.com/watch?v=YcHI_UppicQ&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=3
Oblique asymtotes: Why discard the remainder? http://www.youtube.com/watch?v=jZuZGvUgQj8&list=PLasIAjqJOqkLIkQ3UiSgnutUi24WRp7m6&index=4
Curve Sketching with Rational Functions: http://youtu.be/vgyQMC9Nm_M
Cauchy's Continuity: http://youtu.be/tBuxWO3Hfr0
Introduction to Piecewise Functions: http://youtu.be/GqwlV_KWkBE
Piecewise Functions, Jump Discontinuities, and Limits: http://youtu.be/nyJDuYyfPEQ
VIdeos relevant to trignometry:
Review of Trigonometry: http://youtu.be/mh-x3kNkrhY
Videos relevant to logarithms and exponential functions:
Exponent Laws: http://youtu.be/eIk26nr7ktg
Scientific Notation: http://youtu.be/uZ0ETyx2DkQ
Solving Logarithmic Equations: http://youtu.be/0rcPDgg-BoI
For the techies among you, this video was shot using an el-cheapo Panasonic HMX-F80 I got from an open-box sale for 100 bucks. It stores video in MP4 format. The post-production was done entirely in Linux Ubuntu Studio 13.10 using entirely open-source software, and where practical, open formats such as ogg vorbis were chosen. Voice tracks were recorded using Audacity. The microphone used is part of an inexpensive but good-quality Logitech G330 gaming headset.

Views: 1188
Paul King

Example starts at 4:22 I work through finding the Domain, x-intercept, y-intercept, symmetry, horizontal asymptote, slant asymptote, vertical asymptote and holes, first derivative, intervals of increasing and decreasing, relative maximums and minimums, second derivative, intervals of concave up and down, and finally inflection points. I then finally sketch the graph....phew! Find free review test, useful notes and more at http://www.mathplane.com

Views: 21897
ProfRobBob

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Graphing a Rational Function with Slant / Oblique Asymptote. In this video, I graph a rational function by finding the x and y intercepts, the vertical asymptote, the oblique / slant asymptote and by plotting a few points.

Views: 88085
patrickJMT

Asymptotes of Rational Functions
Watch the next lesson: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/asymptotes-graphing-rational/v/another-rational-function-graph-example?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
https://www.khanacademy.org/math/algebra2/polynomial_and_rational/rational_funcs_tutorial/v/rational-inequalities-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. 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. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. 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. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. 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. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 624251
Khan Academy

This video explains how to determine the equation of horizontal asymptotes of rational functions using the degree of the numerator and denominator. The end behavior is also discussed.
Site: http://mathispower4u
Blog: http://mathispower4u.wordpress.com

Views: 64064
Mathispower4u

B.A B.SC FIRST YEAR CALCULUS OBLIQUE ASYMPTOTES EXERCISE 4.3 BY MONU BHARDWAJ SIR
A+ JULANA
EDUCATION HUB
EDUCATING FOR BETTER FUTURE
A PLUS INSTITUTE OF SCIENCE
APJ INSTITUTE OF SCIENCE

Views: 1383
A Plus Julana - APJ

This lesson describes the process of graphing a rational function that has a slant asymptote. Includes notes and a worked out example.
Clarification: The info wave should begin above the number line only if both the leading coefficient of the denominator and the numerator are positive. If either is negative, the info wave begins below the number line, but still on the right-hand side.
Pre-AP Precalculus lesson created by Stony Point High School Math Department.

Views: 4031
Marcus Lopez

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Vertical Asymptotes of Rational Functions: Quick Way to Find Them, Another Example 1. Just another example of finding vertical asymptotes of rational functions.

Views: 101519
patrickJMT

Using long division of functions to find the exact equation of oblique asymptotes. Two examples are provided.

Views: 140
Sum Math

We work through one example of graphing a rational function with a slant asymptote. We also identify vertical asymptotes, roots and the y-intercept of the rational function. All examples provided by BluePelicanMath.com
For more videos on rational functions see the rational function playlist here: https://www.youtube.com/watch?v=DYqx-SKccho&list=PL_YkQAvGAONhBboPin1u5MhBFpNQ4_Oqh&index=1

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MrHowardMath

For more cool math videos visit my site at http://mathgotserved.com or http://youtube.com/mathsgotserved
Good day students in this clip we are going to be going over two examples on how to find the slant asymptotes of rational funtions ok so let us go ahead and write down the instructions for the examples the task is to find the slant asymptote of the following functions so for number 1 we have the rational function given by y=x^3+1 over x^2+x now if you take a look at this rational function what do you notice about the degree of the numerator and the denominator what you notice is that the degree of the numerator is one more than the degree of the denominator so anytime you have a rational function like this if the degree of the numerator is one higher than the degree of the denominator you will always have a slant asymptote if the degrees are thesame as you know we will have a constant which will be the horizontal asymptote just by dividing the coefficients of the leading terms with equal degrees then if the denominator has a bigger degree then you know that you have a horizontal asymptote of y=0 okay so either you have a horizontal asymptote, slant or other types of asymptotes alright so in this case the degree of the numerator is one greater than the denominator so we are going to have a slant asymptote here so in order to find the slant asymptote all you do is you are going to do the long division you divide the numerator by the denominator and the polynomial portion of your resulting answer is going to be your slant asymptote alright so let us go ahead and set up our long division bars we are going to divide these two polynomials alright so the top goes under the division bar so we are going to write it as x^3 there is no second degree term so we are going to use the place holder 0x^2 there is no first degree term so we use a place holder of 0x plus the constant 1 alright so that is going to be divided by x^2 plus x alright so we always look at the first or leading term of the dividend and the divisor so we have x^2 x^2 goes into x^3 x times so this is the x column right here make sure they line up so you have an x x times squared is x to the third and then x times x is x^2 so this is your standard long division algorithm that I am carrying out here now what you do is you just subtract so we are going to subtract this . Alright so if I subtract that this becomes negative x ^2 and then we can bring that down plus zero x and then we repeat thesame procedure again now x^2 goes into x^2 -1 times x^2 will give you -x^2 and then -1 times x will give you -x. and then you are going to subtract again alright so let us go ahead and subtract put a minus there so -x^2 - -x^2 cancels out and then 0x--x will just give you x plus one alright so the result after we divide is going to be x minus one plus the remainder which is x+1 divided by x^2+x okay put the remainder over the divisor ok now what is your slant asymptote it is the resulting polynomial this linear function right here this is going to be your slant asymptote ok so lets write down what the result is the slant asymptote is given by y=x-1 alright so there you have it alright so this is the graph of the function the rational function that we just worked on finding the slant asymptote of x^3+x/x^2+x this is what it looks like and this is the graph of the slant asymptote that we just found y=x-1 the rise over run and the y intercept is -1 so you can see how the graph of the slant asymptote affects the shape of the curve alright so there you have it. alright let us take a look at another example. question number 2 the task is also to find the slant asymptote of the rational function y=(2x^2+3x+5)/(x+1). do you see why we have a slant asymptote in this situation? absolutely because you notice the degree of the numerator is one more than the degree of the denominator and whenever you have that situation you always have a slant asymptote ok alright so in order for us to find what a slant asymptote is we are going to use long division just as we did in the previous

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maths gotserved

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Rational Functions: Finding Zeros, Asymptotes and Sketching the Graph

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patrickJMT

here i discuss how to find oblique asymptotes. here i tell the working method to solve it. its is topic of bsc maths semester 2

Views: 81900
Manisha Marwaha

How to determine whether the graph of a rational function intersects its horizontal asymptote. This video is provided by the Learning Assistance Center of Howard Community College. For more math videos and exercises, go to HCCMathHelp.com.

Views: 33672
HCCMathHelp

Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and y-intercepts. After finding the asymptotes and the intercepts, we graph the values and then select some random points usually at each side of the asymptotes and the intercepts and graph the points, this enables us to identify the behavior of the graph and thus enable us to graph the function.
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Brian McLogan

In this example, we find the vertical and oblique (slant) asymptotes of a rational function.

Views: 2386
wolferobynm

A discussion of the rules for finding vertical, horizontal, and oblique asymptotes for rational expressions, including examples for each.

Views: 1049
Cathy McFeeters

here i discuss how to find rectangular asymptotes i.e horizontal asymptote and vertical asymptotes and tell the working method to solve it. its is topic of bsc maths semester 2.

Views: 161475
Manisha Marwaha

In this video I go explain what slant asymptotes are and when they arise as well as how to determine what they are for rational functions.
Download the notes in my video: https://www.dropbox.com/s/8a13n84f8qy4qib/161%20-%20Curve%20Sketching%20-%20Slant%20Asymptotes.pdf
Related Videos:
Infinite Limits: Horizontal and Vertical Asymptote Lines and VERY Useful Examples: http://youtu.be/__Y6IRcwdP8
Guidelines to Curve Sketching: http://youtu.be/tOn7ZSAntKs
Polynomials - A Simple Explanation: http://youtu.be/IHIh7Y0kStE
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Polynomial Long Division - Examples: http://youtu.be/7XbzCQgqBPc
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
Graphing with the Google Search Part 1: http://youtu.be/1k3QDg2sB4o .
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Math Easy Solutions