Stitz-Zeager_College_Algebra_e-book

Many students and sadly some instructors will nd it

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Unformatted text preview: = 0 but we know N (0) = 2. (b) The quadratic model for the hours of daylight in Fairbanks, Alaska is y = .51x2 +6.23x − .36. Even with R2 = .92295 we should be wary of making predictions beyond the data. Case in point, the model gives −4.84 hours of daylight when x = 13. So January 21, 2010 will be “extra dark”? Obviously a parabola pointing down isn’t telling us the whole story. Chapter 3 Polynomial Functions 3.1 Graphs of Polynomials Three of the families of functions studied thus far: constant, linear and quadratic, belong to a much larger group of functions called polynomials. We begin our formal study of general polynomials with a definition and some examples. Definition 3.1. A polynomial function is a function of the form: f (x) = an xn + an−1 xn−1 + . . . + a2 x2 + a1 x + a0 , where a0 , a1 . . . . an are real numbers and n ≥ 1 is a natural number.a The domain of a polynomial function is (−∞, ∞). a Recall this means n is a ‘counting number’ n = 1, 2, 3, . . . There are several things about Definition 3.1 that may be off-p...
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