Stitz-Zeager_College_Algebra_e-book

# 1 graphs of polynomials 187 f x 4 x3 1 5 1 3 2 4x 4x

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Unformatted text preview: ing polynomials.) As we shall see in this section, graphs of polynomials possess a quality2 that the graph of h does not. 6. There’s nothing in Deﬁnition 3.1 which prevents all the coeﬃcients an , etc., from being 0. Hence, z (x) = 0, is an honest-to-goodness polynomial. Definition 3.2. Suppose f is a polynomial function. • Given f (x) = an xn + an−1 xn−1 + . . . + a2 x2 + a1 x + a0 with an = 0, we say – The natural number n is called the degree of the polynomial f . – The term an xn is called the leading term of the polynomial f . – The real number an is called the leading coeﬃcient of the polynomial f . – The real number a0 is called the constant term of the polynomial f . • If f (x) = a0 , and a0 = 0, we say f has degree 0. • If f (x) = 0, we say f has no degree.a a 2 Some authors say f (x) = 0 has degree −∞ for reasons not even we will go into. One which really relies on Calculus to verify. 3.1 Graphs of Polynomials 181 The reader may well wonder why we have chosen to se...
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