Name_______________________
Vocabulary
 Degree: the value of the largest exponent
 Leading coefficient: the coefficient of the variable with the largest exponent

End behavior: where the ends of the graphs are approaching
Important things to remember:
 The ends of the graph of a polynomial function with an ___________ degree go in
__________________ directions.

The ends of the graph of a polynomial function with an ___________ degree go in the
______________direction (both up or both down).
 The degree indicates the number of roots a function has.

The degree minus 1 indicates the number of turns the graph of a function has.

Describe the end behavior of each function. State the maximum number of turns the graph of each function could make. State the number of roots (including complex and repeated) each function has. Make a rough sketch of the graph each function.
Example: f (x) = x3 − 4x2 + 4
The leading coefficient is positive and the function has an odd degree:
f(x) → - ∞ as x → - ∞
f(x) → ∞ as x → ∞
The function has a degree of 3:
The graph makes a maximum of 2 turns.
The function has 3 roots.
1. y
 
5 x
2 
3 x 2. f x
 x
3 
4 x
2 
3 x
3. y
   x
2 
3 x

3
5. 125𝑥 3 − 27 = 𝑓(𝑥)
4.
6. y
 
4 x
4 𝑓(𝑥) = 2𝑥 5 − 20𝑥 3 + 18𝑥