7.1_polynomial_functions.ppt
- 1. POLYNOMIAL FUNCTIONS A POLYNOMIAL is a monomial or a sum of monomials. A POLYNOMIAL IN ONE VARIABLE is a polynomial that contains only one variable. Example: 5x2 + 3x - 7
- 2. POLYNOMIAL FUNCTIONS The DEGREE of a polynomial in one variable is the greatest exponent of its variable. A LEADING COEFFICIENT is the coefficient of the term with the highest degree. What is the degree and leading coefficient of 3x5 – 3x + 2 ?
- 3. POLYNOMIAL FUNCTIONS A polynomial equation used to represent a function is called a POLYNOMIAL FUNCTION. Polynomial functions with a degree of 1 are called LINEAR POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 2 are called QUADRATIC POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 3 are called CUBIC POLYNOMIAL FUNCTIONS
- 4. POLYNOMIAL FUNCTIONS EVALUATING A POLYNOMIAL FUNCTION Find f(-2) if f(x) = 3x2 – 2x – 6 f(-2) = 3(-2)2 – 2(-2) – 6 f(-2) = 12 + 4 – 6 f(-2) = 10
- 5. POLYNOMIAL FUNCTIONS EVALUATING A POLYNOMIAL FUNCTION Find f(2a) if f(x) = 3x2 – 2x – 6 f(2a) = 3(2a)2 – 2(2a) – 6 f(2a) = 12a2 – 4a – 6
- 6. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = 3 Constant Function Degree = 0 Max. Zeros: 0
- 7. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x + 2 Linear Function Degree = 1 Max. Zeros: 1
- 8. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x2 + 3x + 2 Quadratic Function Degree = 2 Max. Zeros: 2
- 9. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x3 Cubic Function Degree = 3
- 10. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x4 + 4x3 – 2x – 1 Quartic Function Degree = 4 Max. Zeros: 4
- 11. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x5 + 4x4 – 2x3 – 4x2 + x – 1 Quintic Function Degree = 5 Max. Zeros: 5
- 12. POLYNOMIAL FUNCTIONS END BEHAVIOR Degree: Even Leading Coefficient: + End Behavior: As x -∞; f(x) +∞ As x +∞; f(x) +∞ f(x) = x2
- 13. POLYNOMIAL FUNCTIONS END BEHAVIOR Degree: Even Leading Coefficient: – End Behavior: As x -∞; f(x) -∞ As x +∞; f(x) -∞ f(x) = -x2
- 14. POLYNOMIAL FUNCTIONS END BEHAVIOR Degree: Odd Leading Coefficient: + End Behavior: As x -∞; f(x) -∞ As x +∞; f(x) +∞ f(x) = x3
- 15. POLYNOMIAL FUNCTIONS END BEHAVIOR Degree: Odd Leading Coefficient: – End Behavior: As x -∞; f(x) +∞ As x +∞; f(x) -∞ f(x) = -x3