Polynomial Functions of Higher Degree

Polynomial Functions of Higher Degree - 3.2 Polynomial...

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3.2: Polynomial Functions of Higher Degree So far, we have only graphed two kinds of polynomial functions this semester: lines and parabolas. In this section we will graph polynomials of degree 3 or higher. All polynomial functions have graphs that are smooth continuous curves . In this class, when we say a graph is smooth, we mean that it has no sharp corners. And a graph that is continuous has no holes or breaks. For example, the following graphs are not polynomial functions. (Continuous, but not smooth) (Not continuous) x y x y The General Form of a Polynomial a n x n + a n -1 x n -1 + . . . + a 1 x + a 0 . ˚ a n x n is the leading term , a n is the leading coefficient, and the degree of the polynomial is n Example: P ( x ) = -x 3 + 6 x - 8 the leading coefficient is -1, the degree of the polynomial is 3 F AR- L EFT AND F AR- R IGHT B EHAVIOR n is even n is odd a n > 0 up to the far-left up to the far-right down to the far-left up to the far-right a n < 0 down to the far-left down to the far-right up to the far-left down to the far-right
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Polynomial Functions of Higher Degree - 3.2 Polynomial...

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