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 Algebra  

Rational Expressions - Basic Intro:
   • Rational Expressions - Basic Introduc...  

Simplifying Rational Expressions:
   • Simplifying Rational Expressions  

Multiplying Rational Expressions:
   • Multiplying Rational Expressions  

Dividing Rational Expressions:
   • Dividing Rational Expressions  

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Adding & Subtracting Rational Expressions:
   • Adding and Subtracting Rational Expre...  

Rational Expressions - Unlike Denominators:
   • Adding and Subtracting Rational Expre...  

Simplifying Complex Rational Expressions:
   • Simplifying Complex Rational Expressions  

How To Solve Rational Equations:
   • Solving Rational Equations  

Rational Equations - Extraneous Solutions:
   • Extraneous Solutions of Rational Equa...  

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Horizontal and Slant Asymptotes:
   • Horizontal Asymptotes and Slant Asymp...  

Finding Rational Functions Given 2 Points:
   • How To Find a Rational Function That ...  

Rational Functions - X and Y Intercepts:
   • How To Find The X and Y Intercepts of...  

Graphing Advanced Rational Functions:
   • Graphing Advanced Rational Functions ...  

Rational Inequalities:
   • Rational Inequalities  

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