Polynomial function
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The document defines a polynomial function as a function of the form f(x) = Cnxn + Cn-1xn-1 + ... + C3x3 + C2x2 + C1x + C0, where Cn, Cn-1,...C3,C2,C1,C0 are constants and Cn ≠ 0, and n is a non-negative integer called the degree of the polynomial function. Some examples of polynomial functions of specific degrees are provided, including linear functions which are of degree 1 and quadratic functions which are of degree 2. The document also provides examples of functions that are not polynomial functions and examples of polynomial functions with their degrees identified based on the term
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Polynomial function
- 2. WOODGROVE BANK 2 • If f(x) = CnXn + Cn-1Xn-1 + … + C3X3 + C2X2 + C1 X + C0, where Cn, Cn-1, ,… C3, C2, C1, C0 are constants and Cn ≠ 0 and n is a non-negative integer then f(x) is called a polynomial function of degree n. • A linear function is a polynomial function of degree 1. • A quadratic function is a polynomial function of degree 2. • A cubic function is a polynomial function of degree 3. • The degree of a polynomial function is the degree of the term with the highest degree.
- 3. WOODGROVE BANK 3 Polynomial Functions Not Polynomial Functions 1. F(x) = x + 2 2. F(x) = 3x – x + 5-3 3. F(x) = (x + 3)(x – 1) = x2 + 2x - 3 4. F(x) = 4(x2 – 1) 5. F(x) =x(x5 – 6) 1. x-2 + 2 2. 4x1/3 – 6 3. 2x −1 x 4. x - 6 = 3 5. 3y 2y+4
- 6. WOODGROVE BANK 6 Polynomial Functions Degree Leading Term 1. F(x) = x3 – 2x + 5 3 x3 2. F(x) = x2y – 3x – 1 3 x2y 3. F(x) = 2x4 – x5 + 3 5 x5 4. F(x) = 7 – 2x – x6 6 x6 5. F(x) = x3y2 + 27 5 x3y2