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Unformatted text preview: between the right- and left-end behaviors of the polynomial. They are also solutions to the equation f ( x ) = 0. Moreover, they determine factors of the functions: if c , a real number, is a zero of f , then x-c is a factor of f ( x ). There are two types of zeros of a polynomial: 1. Zeros of even multiplicity. 2. Zeros of odd multiplicity. Examples: Find the zeros of each polynomial and determine the multiplicity of each zero: 1. g ( x ) = x 4-4 x 2 2. h ( x ) =-4 x 3 + 4 x 2 + 15 x Fact: A polynomial of degree n has at most n-1 turning points. Intermediate Value Theorem: Let a and b be real numbers such that a < b . If f is a polynomial function such that f ( a ) 6 = f ( b ), then in the interval [ a, b ] f takes on every value between f ( a ) and f ( b ). Examples: Sketch the graph of the function: 1. g ( x ) = x 4-4 x 2 2. h ( x ) =-4 x 3 + 4 x 2 + 15 x...
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- Fall '10
- Algebra, Continuous function