Horizontal and Vertical Asymptotes - Slant / Oblique - Holes - Rational Function - Domain & Range

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.
Fundamental Theorem of Algebra:
• Fundamental Theorem of...
Rational Expressions - Basic Intro:
• Rational Expressions -...
Simplifying Rational Expressions:
• Simplifying Rational E...
Multiplying Rational Expressions:
• Multiplying Rational E...
Dividing Rational Expressions:
• Dividing Rational Expr...
______________________________________
Adding & Subtracting Rational Expressions:
• Adding and Subtracting...
Rational Expressions - Unlike Denominators:
• Adding and Subtracting...
Simplifying Complex Rational Expressions:
• Simplifying Complex Ra...
How To Solve Rational Equations:
• Solving Rational Equat...
Rational Equations - Extraneous Solutions:
• Extraneous Solutions o...
_____________________________________
Horizontal and Slant Asymptotes:
• Horizontal Asymptotes ...
Finding Rational Functions Given 2 Points:
• How To Find a Rational...
Rational Functions - X and Y Intercepts:
• How To Find The X and ...
Graphing Advanced Rational Functions:
• Graphing Advanced Rati...
Rational Inequalities:
• Rational Inequalities
________________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

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At 8:05 you stated that -1 + 7 = -6. You graphed it correctly but it should have been positive 6.

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Ye however the graph would basically be the same sketch as positive 6 still below the horizontal asymptote (7)

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Explanations to find vertical and horizontal asymptotes as well as slant asymptotes are clear and understandable. Thank you.

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[@renewd]

For the 2nd example, y = 1/(x + 2) + 7, I had never tried to graph a rational expression with a constant added to it. I went ahead and rewrote it as y = (7x + 15)/(x + 2) using a common denominator, and then found the horizontal asymptote to be 7x/x = 7/1 = 7, so y = 7. It was interesting to know that it is the same as y = 0 shifted up 7.

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We owe you a lot! Amazing teacher! At 8:05 you stated that -1 + 7 = -6. You graphed it correctly but it should have been positive 6.

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Your videos are very helpful to me, but I noticed an error @8:00 mins where you said -1 + 7 = -6, it should be +6, which has a cascading effect. But I'm still watching, your style is helpful.

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great video but you should consider when the graph is able to cross the HA since the graph of a rational function can have a hole but it does not have to pass through it.

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at the time 22:51 -- I calculated the zeros x= -1/2 however you plot the curve touching around 1.5 as a zero. I just wanted to check if you were doing the rough sketch or I was calculating it wrong on Zeros for this problem. Thanks advance.

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