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 contains plenty of examples and practice problems.
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...
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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...
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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
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Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

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[@georgesadler7830]

MR. Organic Chemistry Tutor, this is another solid explanation of Graphing Rational Functions Using Transformations with Vertical and Horizontal Asymptotes. These concepts are fairly easy to understand. Over the years, I tutor this class at the Community College of Baltimore County in Catonsville, Maryland. I really learned this class by teaching it to many different students.

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[@frutchiedeen9902]

How would you graph this kind of function if it has a numerator greater than one? That’s my only question. The rest of the video was extremely helpful, thank you!

[@TheThreadshitter]

For a rough sketch, not particularly different. More accurately, the curved parts wouldn't be as close to the asymptotes, especially at the places where vertical and nonvertical asymptotes meet. The numerical numerator is a stretching factor, we can say.

[@Leviathan12]

@@TheThreadshitter Would y=1/x -> y=3/x be a vertical shrink or stretch?

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can you do more explanation about how to draw asymptotes

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[@futbolyou4129]

at 8:20 why is the horizintal Asymptote 0?

[@zachadolphe3633]

for y = (1/x^2) -3 shouldn't the graph show going to negative infinity as x approaches zero from the left and be below the -3 HA?

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X cannot be negative

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hey, your las exercise, I thought when you have the difference of two squares you make x=2 and x=-2 making two vertical asymptotes instead of one

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y = 1/(1 - x) What is the graph of this equation?

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4:54 shouldn't it be (0, negative infinity)?

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Negative numbers are on the left side of zero, so it's (-infinity,0)

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9:32

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