3.1_Exploring.Polynomials_student

3.1_Exploring.Polynomials_student - st differences are...

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MHF 4U0 3.1 Exploring Polynomial Functions A polynomial function is a function that has the form f(x) = a n x n + a n–1 x n–1 + … + a 2 x 2 + a 1 x + a o , where: a n , a n-1 , … are real numbers n is a positive integer ( n is called the degree of the polynomial) Example #1: Which of the following functions are polynomials? State the degree for each polynomial. Function Polynomial? (Yes/No) Degree 4 2 3 ) ( 2 - + = x x x f 2 6 4 ) ( x x x g + - = 2 ) ( - = x x h x x x k 1 ) ( 3 + = 1 3 ) ( - = x x m x x p = ) ( x x q 4 ) ( = 9 6 3 1000 ) ( x x x r + - = SUMMARY: The domain of a polynomial function is the set of all real numbers. The range of a polynomial function may be all real numbers, or it may have a lower bound or an upper bound (but not both). The graphs of polynomial functions do not have horizontal or vertical asymptotes. The n th finite differences of a polynomial function of degree n are constant. o Linear functions => 1
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Unformatted text preview: st differences are constant o Quadratic functions => 2 nd differences constant o Cubic functions => 3 rd differences constant o and so on! pg. 1/3 MHF 4U0 pg. 2/3-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10-10-8-6-4-2 2 4 6 8 10 MHF 4U0 Linear: f(x) = x Domain: Range: Asymptotes: Quadratic: f(x) = x 2 Domain: Range: Asymptotes: Cubic: f(x) = x 3 Domain: Range: Asymptotes: Quartic: f(x) = x 4 Domain: Range: Asymptotes: Quintic: f(x) = x 5 Domain: Range: Asymptotes: pg. 3/3...
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This note was uploaded on 01/14/2012 for the course MAT 107 taught by Professor Sda during the Spring '11 term at Beacon FL.

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3.1_Exploring.Polynomials_student - st differences are...

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