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# 1140 L14 - f(x = |x| f(x = x 2/3 f(x = cfw_1 x x<0 x>0

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Lecture 14, Part I: Section 2.2 Polynomial Functions of Higher Degree A polynomial function of degree n has a form f ( x ) = a n x n + a n 1 x n 1 + + a 1 x + a 0 where a n ; a n 1 ; : : : ; a 1 ; a 0 are real numbers, where a n 6 = 0 and n 0 is an integer . Graph of a Polynomial Function The graph of a polynomial function is one continuous and smooth curve. NOTE: continuous : no holes, gaps or breaks, smooth : no sharp corners or cusps Examples of non-polynomial graphs: > 0 < 0 x x 1 x { 2/3 f(x) = f(x) = |x| f(x) = x

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Power Functions Def. A power function of degree n is a monomial function of the form f ( x ) = x n where n > 0 is an integer. ex. Graph of y = x n , where n is even : ex. Graph of y = x n , where n is odd :
NOTE: 1. If n is even , the graph is symmetric w.r.t. the y axis and touches the x -axis at its x -intercept. 2. If n is odd , the graph is symmetric w.r.t. the origin and crosses the x -axis at its x -intercept. 3. As n increases, the graph of y = x n becomes narrower for j x j > 1, but is atter where j x j < 1.

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1140 L14 - f(x = |x| f(x = x 2/3 f(x = cfw_1 x x<0 x>0

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