![POLYNOMIAL FUNCTIONS
EVALUATING A POLYNOMIAL FUNCTION
Find 2g(-2a) if g(x) = 3x2
– 2x – 6
2g(-2a) = 2[3(-2a)2 – 2(-2a) – 6]
2g(-2a) = 2[12a2 + 4a
– 6]
2g(-2a) = 24a2 + 8a](https://image.slidesharecdn.com/introductiontopolynomialfunctions-250807065428-b00147f9/85/Introduction-to-polynomialfunctions-pptx-16-320.jpg)
Introduction to polynomialfunctions.pptx
- 2. 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
- 3. A polynomial function is a function of the form n – 1 n A polynomial function is in standard form if its terms are written in descending order of exponents from left to right. is the a0 Where aan 00 and the exponents are all whole numbers. ann n n For this polynomial function, aann leading coefficient, a0 is the ccoonnssttaanntt tteerrmm, and n n is the ddeeggrreeee. descending order of exponents from left to right. f (x) = x n + an – 1 x n – 1+· · ·+ a 1 x + a 0 a 0
- 4. 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 ?
- 5. 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
- 6. Degree Type Standard Form 0 Constant f (x) = a 0 1 Linear f (x) = a1x + a 0 2 Quadratic 2 f (x) = a 2 x + a 1 x + a 0 3 Cubic 3 2 f (x) = a 3 x + a 2 x + a 1 x + a 0 4 Quartic 4 3 2 f (x) = a4 x + a 3 x + a 2 x + a 1 x + a 0 You are already familiar with some types of polynomial functions. Here is a summary of common types of polynomial functions.
- 7. Polynomial Functions The largest exponent within the polynomial determines the degree of the polynomial. Polynomial Function in General Form Degree Name of Function y ax b 1 Linear y ax 2 bx c 2 Quadratic y ax3 bx 2 cx d 3 Cubic y ax 4 bx3 cx 2 dx e 4 Quartic
- 8. Identifying Polynomial Functions Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type and leading coefficient. f (x) = 1 x 2 – 3x4 – 7 2 SOLUTION The function is a polynomial function. The leading coefficient is – 3. Its standard form is f (x) = – 3x 4 + 1 x 2 – 7. 2 It has degree 4, so it is a quartic function.
- 9. Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type and leading coefficient. Identifying Polynomial Functions f (x) = x 3 + 3 x SOLUTION The function is not a polynomial function because the term 3 x does not have a variable base and an exponent that is a whole number.
- 10. Identifying Polynomial Functions Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type and leading coefficient. f (x) = 6x 2 + 2 x –1 + x SOLUTION The function is not a polynomial function because the term 2x –1 has an exponent that is not a whole number.
- 11. Identifying Polynomial Functions Decide whether the function is a polynomial function. If it is, write the function in standard form and state its degree, type and leading coefficient. f (x) = – 0.5 x + x 2 – 2 SOLUTION The function is a polynomial function. Its standard form is f (x) = x2 – 0.5x – 2. It has degree 2, so it is a quadratic function. The leading coefficient is .
- 12. f (x) = 1 x 2 – 3 x 4 – 7 2 Identifying Polynomial Functions Polynomial function? f (x) = x 3 + 3x f (x) = 6x2 + 2 x– 1 + x f (x) = – 0.5x + x2 – 2
- 13. 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
- 14. 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
- 15. POLYNOMIAL FUNCTIONS EVALUATING A POLYNOMIAL FUNCTION Find f(m + 2) if f(x) = 3x2 – 2x – 6 f(m + 2) = 3(m + 2)2 – 2(m + 2) – 6 f(m + 2) = 3(m2 + 4m + 4) – 2(m + 2) – 6 f(m + 2) = 3m2 + 12m + 12 – 2m – 4 – 6 f(m + 2) = 3m2 + 10m + 2
- 16. POLYNOMIAL FUNCTIONS EVALUATING A POLYNOMIAL FUNCTION Find 2g(-2a) if g(x) = 3x2 – 2x – 6 2g(-2a) = 2[3(-2a)2 – 2(-2a) – 6] 2g(-2a) = 2[12a2 + 4a – 6] 2g(-2a) = 24a2 + 8a
- 17. Divide and WRITE
- 19. Examples of Polynomial Functions
- 20. Examples of Nonpolynomial Functions