1. Algebra II Section 5-3
Polynomial Functions

2. Vocabulary: Polynomial - monomial or a sum of monomials
Polynomial function -
f(x) = anxn + an-1xn-1 + … + a1x + a0
exponents are ________________________
coefficients are ________________________
only one variable per problem

3. Standard form: - terms are written in descending order of __________________________ Leading Coefficient: - when the polynomial is written in standard form it is the first coefficient - the coefficient of the ___________________

4. Degree: - the value of the highest __________________ when there is a single variable
Degree  Name
0  constant
1  linear
2  quadratic
3  cubic
4  quartic
5  quintic

5. State whether the function is a polynomial
State whether the function is a polynomial. If so, write it in standard form and state its degree and leading coefficient. 1. f(x) = 6x½ - 5x

6. State whether the function is a polynomial
State whether the function is a polynomial. If so, write it in standard form and state its degree and leading coefficient. 2. 𝑔 𝑥 = −8 𝑥 5 −4 𝑥 𝑥 4

7. State whether the function is a polynomial
State whether the function is a polynomial. If so, write it in standard form and sate its degree and leading coefficient. 3. 𝑓 𝑥 = 𝑥 3 − 4 5 𝑥 2 − 1

8. State whether the function is a polynomial
State whether the function is a polynomial. If so, write it in standard form and sate its degree and leading coefficient. 4. g(x) = - 3x4 - 9x x4

9. Evaluate the function at the given values. 5a. 𝑔 𝑥 = 𝑥 2 −5𝑥+8 𝑔 =

10. Evaluate the function at the given values. 5b. 𝑔 𝑥 = 𝑥 2 −5𝑥+8 𝑔 =
Algebra II Sec 5-3
Evaluate the function at the given values. 5b. 𝑔 𝑥 = 𝑥 2 −5𝑥+8 𝑔 =

11. 6a. 𝑔 𝑥 = 𝑥 2 −5𝑥+8 4𝑔 =

13. 6b. 𝑔 𝑥 = 𝑥 2 −5𝑥+8 𝑔 + 3𝑔( )=

15. End Behavior: - describes the direction the graph is going at each _________________ - look from the origin out (to the left and right) - notation: 𝑓 𝑥 → + ∞ 𝑎𝑠 𝑥 →− ∞ 𝑓 𝑥 →− ∞ 𝑎𝑠 𝑥 →+ ∞

16. - degree shows the ______________ number of times the graph may intersect the ___________________________ - even functions have the ____________ end behavior on both sides - odd functions have the __________________ end behaviors

18. For each graph: describe the end behavior, determine whether it represents an odd-degree or an even-degree polynomial, and state the number of zeros. 7.

19. For each graph: describe the end behavior, determine whether it represents an odd-degree or an even-degree polynomial, and state the number of zeros. 8.

20. For each graph: describe the end behavior, determine whether it represents an odd-degree or an even-degree polynomial, and state the number of zeros. 9.

21. For each graph: describe the end behavior, determine whether it represents an odd-degree or an even-degree polynomial, and state the number of zeros. 10.

22. For each graph: describe the end behavior, determine whether it represents an odd-degree or an even-degree polynomial, and state the number of zeros. 11.