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Section 4.5 - Section 4.5 Rational Functions Recall a...

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Section 4.5 Rational Functions Recall, a rational number is any number that can be written as a fraction. A rational function is a function that is a fraction. A rational function is a function f that is a quotient of two polynomials. Then is, where p(x) and q(x) are polynomials and where q(x) is not the zero polynomial. the domain of f consists of all inputs x for which q(x) 0. See pictures p. 342. Finding Asymptotes Asymptotes are imaginary lines the graph of a rational function approaches. They are useful when sketching the graph of a rational function. Asymptotes may be vertical, horizontal or oblique (slant). Your calculator will show vertical and oblique asymptotes but not horizontal asymptotes. Remember the equation of a vertical line is x = a # and the equation of a horizontal line is y = a #. See pictures p. 345, 346, 350. To find asymptotes: Reduce rational functions to lowest terms, if possible, by factoring and cancelling.
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