1. Graphing Polynomial Functions
Learning Targets:
• Graph polynomial functions by hand or using technology, identifying zeros when suitable factorizations are available, and showing end behavior.
• Recognize even and odd functions from their algebraic expressions.

2. Terms:
Degree – The exponent or total of exponents on the largest monomial.
Polynomial – Made of monomials (No variable exponents, no negative exponents or fractional exponents).
Standard Form of a Polynomial – Written with the largest exponent in descending order.
Leading Coefficient – The # on the 1st term.

3. Features of a Polynomial Function Graph
1. A continuous graph.
2. Has only smooth turns. (The maximum number of turns is the degree minus 1)
3. Leading Coefficient: (The Right Side of the Graph)
A. Positive: The graph rises to the right.
B. Negative: The graph falls to the right.
4. Degree: (The Left Side of the Graph)
A. Even: The left behavior is the same as the right behavior.
B. Odd: The left behavior is the opposite of the right behavior.

4. Examples: Determine if the function is a polynomial
Examples: Determine if the function is a polynomial. If yes, write in standard form, state the degree, type, and the leading coefficient. 1. No
-2 exponent 2.
Yes,
,Degree=4,
Quartic,
Leading coefficient=1
Turns:
Right Behavior:
Left Behavior:
3 max
Lead Coefficient (1)
Positive=Rises
Degree (4) even,
same behavior (rises)

5. 3. Graph Turns: (3-1) 2 Maximum Leading Coefficient:
(1)positive—right side rises
Degree:
(3) odd, left side is opposite (falls)

6. 4. Graph Turns: (3-1) 2 Maximum Leading Coefficient:
(-1)negative, right side falls
Degree:
(3) odd, left side is opposite (rises)
Roots:
(3 total) -2, 1, 1
Local Max:
(.9999, 0)
Local Min:
(-.9999, -4)