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Unformatted text preview: n share two properties which help distinguish them from other animals in the algebra zoo: they are continuous and smooth. While these concepts are formally defined using Calculus,15 informally, graphs of continuous functions have no ‘breaks’ or ‘holes’ in their graphs, and smooth functions have no ‘sharp turns.’ It turns out that these traits are preserved when functions are added together, so general polynomial functions inherit these qualities. Below we find the graph of a function which is 13 We ignore the case when n = 1, since the graph of f (x) = x is a line and doesn’t fit the general pattern of higher-degree odd polynomials. 14 And are, perhaps, the inspiration for the moniker ‘odd function’. 15 In fact, if you take Calculus, you’ll find that smooth functions are automatically continuous, so that saying ‘polynomials are continuous and smooth’ is redundant. 3.1 Graphs of Polynomials 185 neither smooth nor continuous, and to its right we have a graph of a polynomial, for comparison. The function whose graph appears on the left fails to...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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