{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3.1_Exploring.Polynomials_student

# 3.1_Exploring.Polynomials_student - st differences are...

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}