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Rational Functions - Math

Rational FunctionsIn this chapter, you ll learn what a Rational function is, and you ll learnhow to sketch the graph of a Rational functionsArational functionis a fraction of polynomials. That is, ifp(x)andq(x)are polynomials, thenp(x)q(x)is a Rational function. Thenumeratorisp(x)andthedenominatorisq(x ).Examples. 3(x 5)(x 1) 1x 2x31=2x3 The last example is both a polynomial and a Rational function. In a similarway, any polynomial is a Rational this class, from this point on, most of the Rational Functions that we ll seewill have both their numerators and their denominators completely will also only see examples where the numerator and the denominatorhave no common factors. (If they did have a common factor, we could justcancel them.)**Implied domainsThe implied domain of a Rational function is the set of all real numbersexceptfor the roots of the denominator.

will have both their numerators and their denominators completely factored. We will also only see examples where the numerator and the denominator have no common factors. (If they did have a common factor, we could just cancel them.) ***** *** Implied domains The implied domain of a rational function is the set of all real numbers

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