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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.

In other words, ↵ is a root of p(x). Thus, the roots of the numerator are exactly the x-intercepts. Example. 2istheonlyx-intercept of the rational function 7(x2)(x2 +1) 8(x4)(x6) ***** *** In between x-intercepts and vertical asymptotes When graphing a rational polynomial, first mark the vertical asymptotes and the x-intercepts.

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