Transcription of 2.4Polynomial and Rational Functions Polynomial Functions
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2.4Polynomial and Rational Functions Polynomial Functions
Polynomial and Rational FunctionsPolynomial FunctionsGiven a linear functionf(x) =mx+b, we can add a square term, andget a quadratic functiong(x) =ax2+f(x) =ax2+mx+b. We cancontinue adding terms of higher degrees, we can add a cube termand geth(x) =cx3+g(x) =cx3+ax2+mx+b, and so (x),g(x),andh(x) are all special cases of a Polynomial ( Polynomial Function)Apolynomial functionis a function that can be written in theformf(x) =anxn+an 1xn 1+..+a1x+a0forna nonnegative integer, called thedegreeof the coefficientsan, an 1, .. , a1, a0are real numbers withan6= that althoughan6= 0, the remaining coefficientsan 1, an 2.
Ch 2. Functions and Graphs 2.4 Polynomial and Rational Functions De nition (Leading Coe cient) Given a polynomial function f(x) = a nxn+a n 1xn 1+:::+a 1x+a 0, the coe cient a
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