Graphing Rational Functions With Vertical, Horizontal & Slant Asymptotes, Holes, Domain & Range

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.
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...
_____________________________________
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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0:10 y=1/x -- 2:10 y=1/x^2 4:30 y=1/x-1 11:36 y=(1/x+2)-3 16:30 Graphs of y=1/x 17:54 y=(-1/x+2)+3 22:13 y=(1/(x-2)^2)+1 24:44 y=(-1/(x+1)^2)+2 28:00 HA OF same degree functions 30:44 HA of bottom heavy 31:47 y=((2(x-2))/(x-3) 35:35 y=(3x^2+9x-12)/(x^2+x-2) 44:40 Slant asymptote y=(2x^2+6x-8)/(x-2)

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00:00 Degree of denominator is higher than the numerator. 28:05 Degree of denominator is the same as the numerator. 30:50 Degree of numerator is greater than the denominator.

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Your videos to watch are always helpful. I always search you up for Math topic explanations. For a problem, time on the video (10:47 to 11:05), you mentioned the domain as (- ∞,-1) ∪(-1, ∞). However, I feel it should be 1 in the domain not -1

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Im SOOOO glad you added that -3 at 11:43. I've been looking for an example that affects HA, now I know how to interpret it. Thanks a lot!

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046

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at 11:15 the domain should be (-in,1) U (1,in) correct me if I'm wrong.

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9

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Hi! Mr.chemistry tutor, I think the domain of the function in 11:26 is 1 not -1. The Vertical asymptote is x=1.

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@@maryyou556 1/x-1. x=1. 1 renders the denominator 0. 1 is the VA. What is throwing you off is that he got the domain wrong.

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