1. Do Now: Evaluate the function for the given value of x.
1. f x   7x − 6; x  − g x   x 2  3; x  6
3. f x   −3x  4; x  − g x   x 2 − 6x ; x  − 4

2. Algebra II 4.1: Graphing Polynomial Functions
Objective: To identify polynomials, and to use several techniques to get rough sketches.

3. Vocabulary What is a monomial?
An expression that is either a number, a variable, or the product of a number and one or more variables

4. Vocabulary
What is a Polynomial?
A monomial or a sum of monomials

5. A polynomial function is in standard form when its terms are written in descending order of exponents from left to right.

6. Vocabulary Polynomial Function = a function in the form:
n is the degree or the highest exponent.
is the leading coefficient.
is the constant term.

7. the exponents are all whole numbers
What is a whole number?
the coefficients are all real numbers
What is a real number?

8. Common Polynomial Functions
Degree
Type
Example
Constant
f(x)=-14 1
Linear
f(x)=5x – 7 2
Quadratic
f(x)=2x2+x-9 3
Cubic
f(x)=x3-x2+3x 4
Quartic
f(x)=x4+2x – 1

9. Think-Pair-Share: Write your own
Degree
Type
Example 3
Constant
Quartic
f(x)=-x4+3x2+5
f(x)=-11x+24
Quadratic

10. Example 1

11. Decide whether the function is a polynomial function
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

12. Decide whether the function is a polynomial function
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

13. Example 2
Evaluate f (x ) = 2x 4 − 8x 2 + 5x − 7 when x = 3.

14. Closing
Exit Ticket: State the degree, type, and leading coefficient of the following function, then an example of a polynomial with those same characteristics.
f (x ) = 3.5x 4 + 4x 2 − 7x + 2

15. Homework:
Textbook page 162 # 4-16 evens