# L14 - Lecture 14 Part I Section 2.2 Polynomial Functions of...

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Unformatted text preview: Lecture 14, Part I: Section 2.2 Polynomial Functions of Higher Degree A polynomial function of degree u1D45B has a form u1D453 ( u1D465 ) = u1D44E u1D45B u1D465 u1D45B + u1D44E u1D45B − 1 u1D465 u1D45B − 1 + ⋅⋅⋅ + u1D44E 1 u1D465 + u1D44E where u1D44E u1D45B , u1D44E u1D45B − 1 , . . . , u1D44E 1 , u1D44E are real numbers, where u1D44E u1D45B ∕ = 0 and u1D45B ≥ 0 is an integer. u1D453 ( u1D465 ) = 0; zero polynomial, degree = none u1D453 ( u1D465 ) = u1D450 ; constant, degree = 0 u1D453 ( u1D465 ) = u1D44Eu1D465 + u1D44F ; linear, degree = 1 u1D453 ( u1D465 ) = u1D44Eu1D465 2 + u1D44Fu1D465 + u1D450 ; quadratic, degree = 2 Graph of a Polynomial Function The graph is continuous : no holes, gaps or breaks The graph is smooth : no sharp corners or cusps > 0 < 0 x x 1 x { 2/3 f(x) = f(x) = |x| f(x) = x Power Functions Def. A power function of degree u1D45B is a function of the form u1D453 ( u1D465 ) = u1D44Eu1D465 u1D45B where u1D44E is a nonzero real number and u1D45B > 0 is an integer. ex. u1D466 = u1D465 u1D45B , where u1D45B is even: ex. u1D466 = u1D465 u1D45B , where u1D45B is odd: NOTE: 1. If u1D45B is even, the graph touches the u1D465-axis at its u1D465-intercept. 2. If u1D45B is odd, the graph crosses the u1D465-axis at its u1D465-intercept....
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L14 - Lecture 14 Part I Section 2.2 Polynomial Functions of...

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