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PP Section 4.6 - PolynomialFunctions A polynomial function...

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Polynomial Functions
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A polynomial function is a function of the form f x a x a x a x a n n n n ( ) = + + + + - - 1 1 1 0 where a n , a n-1 ,…, a 1 , a 0 are real numbers and n is a nonnegative integer. The domain consists of all real numbers. The degree of the polynomial is the largest power of x that appears.
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Example : Determine which of the following are polynomials. For those that are, state the degree. (a) f x x x ( ) = - + 3 4 5 2 Polynomial of degree 2 (b) h x x ( ) = - 3 5 Not a polynomial (c) F x x x ( ) = - 3 5 2 5 Not a polynomial
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A power function of degree n is a function of the form n n x a x f = ) ( where a is a real number, a not 0, and n > 0 is an integer. Examples: 4 3 ) ( x x f = 7 5 ) ( x x f - =
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even , 0 , ) ( n a ax x f n = Symmetric with respect to the y -axis. Domain is the set of all real numbers. Range is the set of nonnegative real numbers. What changes if a < 0?
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odd , 0 , ) ( n a ax x f n = Symmetric with respect to the origin. Domain is the set of all real numbers. Range is the set of all real numbers.
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