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

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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.

Domain and Range - Free Formula Sheet:


Fundamental Theorem of Algebra:


Rational Expressions - Basic Intro:


Simplifying Rational Expressions:


Multiplying Rational Expressions:


Dividing Rational Expressions:


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Adding & Subtracting Rational Expressions:


Rational Expressions - Unlike Denominators:


Simplifying Complex Rational Expressions:


How To Solve Rational Equations:


Rational Equations - Extraneous Solutions:


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Horizontal and Slant Asymptotes:


Finding Rational Functions Given 2 Points:


Rational Functions - X and Y Intercepts:


Graphing Advanced Rational Functions:


Rational Inequalities:


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