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Rational Functions

 Topic Review on "Title": Rational functions:  Any function which can be written of the form: where and are polynomials. Domain of a rational function: The set of points where the function is defined. Vertical asymptote: A line of the form such that takes arbitrarily large values near Horizontal asymptote: A line of the form such that if tends to infinity, tends to  The sum of rational functions: . The product of rational functions: . Simple functions Simple functions are rational functions that cannot be simplified any further. The division of rational functions: .

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 "Title" Tutorial Summary : This tutorial describes rational functions and their properties. The domain of rational functions is described with the use of horizontal and vertical asymptotes. The degrees of the two functions composing of a rational function are important to find the asymptotes of rational functions. This tutorial describes the operation of rational functions with the use of examples. A rational function can be simplified by factoring the numerator function of rational functions and the denominator function of rational functions. Solving rational equations involves comparing the degrees and evaluating both functions so simplification can be achieved as much as possible.

 Tutorial Features: Specific Tutorial Features: • Rational functions are reduced using simplification techniques. • The asymptotes of rational functions are shown in some of the examples. Series Features: • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced. • Definition slides introduce terms as they are needed. • Visual representation of concepts • Animated examples—worked out step by step • A concise summary is given at the conclusion of the tutorial.

 "Title" Topic List: `Rational functions and their basic definitions The domain of rational functions Rational functions and their asymptotes FormulasThe operations of rational functions Simple rational functions Simplification of rational functionsPolynomial equations Polynomial equations and their solutions`

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